Originality: 3.0 Blood Magus. Yeah. I'm not just taking off points because there were three Blood Magi. I'm taking off points because there were three Blood Magi and Blood Magus was the very first thing I thought of when I read Polyhaemia. (Plus, the fact that it's got overlapping prereqs and offers Heal as a class skill makes it a pretty natural choice for Flux Adept.) So you've got the double whammy of it being obvious and it being repeated. [–0.5] Beyond that, though, I definitely didn't expect a Barbarian, and even though we were already in the Dragon Compendium, I didn't expect a (pair of) dvati either. I have no idea why you're doing either of those things, but the fact remains that I didn't expect them at all, so I can give you points for that. [+0.5] Using Precocious Apprentice to get "2nd level spells" with only one level expended is gutsy, but it's also not exactly anything new.
Power: 1.75 Using dvati to get your HP down low enough to have Berserker Strength active is . . . I'm going to say clever. Too clever by half, perhaps, but clever. That said, is it actually wise to have HP so low that you can rely on that? You're getting up close and personal with the enemies, you've got no CON bonus, and you're at half HP compared to a regular character to begin with (plus, you're a level behind thanks to your LA, so your HP is even lower than usual compared to a normal character). And of course, you mentioned that you're using Blood Magus to self-damage with the express goal of getting into Berserker Strength. You also have low AC (no DEX, I'm not sure what kind of armor you actually wear, and Berserker Strength imposes a –2, as you mentioned). What prevents you from just keeling over the first time something decides that you look squishy? I guess you do have a few basic defensive spells (Mage Armor, Mirror Image, Displacement, Fire Shield), but aside from Mage Armor, all of those take actions in combat (from both twins, mind you), and I don't see any way of reducing that action cost, assuming that you can even concentrate to cast them (see my comments in Elegance). (It also doesn't help that you have to occupy both twins to cast those spells.) Plus, it's an awfully long time before you actually have enough spellcasting mojo to have the slots and CL available for those things, so you're definitely a few steps behind a normal "squishy Wizard," who wouldn't normally be Power Attacking things in melee range. Tempting Fate only works once per day (and only on one twin!), and there's a lot of levels before it comes online (even assuming you can get a bonus luck feat from the Court of Thieves, which I really don't like you relying on in an Iron Chef context, especially given that I'm not at all sure how you would actually get past the gauntlet of traps that protects the Court of Thieves). I do see Diehard in there, which I guess kind of works with Stanch from Blood Magus, but really, that's kind of weak tea (and it might make you even more likely to be killed, since someone standing and fighting as an active combatant at negative HP is more likely to get knocked to –10 than someone who's unconscious and therefore no longer a threat—and remember that Feign Death takes a standard action, so you can't just fall over and play dead in response to someone hitting you). Overall, I just don't see how you can actually survive your primary strategy of Berserk-ly meleeing things in the face, and that makes me think that you just aren't that effective at what you profess to do. [–0.75]
You seem to be relying a fair bit on using Handle Animal to take care of things for you (you mention training magebred combat animals into Warbeasts, loadstone marauders, and warbeast sparrows, I believe?), but your Handle Animal is really nothing special. I don't know how many ranks you actually have in it (since you didn't actually finish your skill points), but you don't have that many to begin with (and it looks like you have one point free per Flux Adept level, which you're somehow splitting between four different skills?), you have 8 CHA, and Pheromonic Control is only worth a +4 at best (limited times per day for the Eagle's Splendor part, and only against things with Scent for the other part). I can't tell just how much of your primary strategy actually relies on this, but I don't see you as actually being good at it. Since you mention it in three separate areas in your entry, I figure you care about it enough that it kind of matters whether or not you're actually good at it. [–0.25]
I'm incredibly skeptical that you can use your familiar to do all the work for you that you think it can do. With no ranks in Diplomacy, why should anyone actually listen to a weird talking semi-draconic animal thing (of indeterminate type, since you didn't specify cat vs. raven vs. huitzl) to find hirelings or train teamwork benefits or purchase trainable animals or introduce a pair of weird (constantly raging) Things to a party? (We're not even going to talk about them somehow setting up your whole Court of Thieves escapade.) I do understand that this is D&D, so I'm not saying that no one would ever listen to a weird semi-draconic talking animal, but I'm still highly skeptical that you can just use your familiar as a proxy to do everything you think it can do. As a result, I think your out-of-combat abilities are more limited than you're admitting. I'm not going to hand out a penalty in that regard (since I do appreciate you at least acknowledging that you'll need some flavor of workaround for those levels where you're literally always raging), but neither am I going to award any bonuses for that sort of thing. At best, you're half-covering a weakness; I don't see enough of a positive strength here to be worthy of a bonus. 
I'm not seeing a lot of utility coming from your magic. You seem to mostly have combat spells, but with your super-slow progression and your limited ability to cast thanks to Berserker Strength, I'm not sure how often you can bring those spells to bear. What's more, you have no ranks in Concentration or Tumble, so if you're in melee range of something you can't 5 ft step away from, you WILL get attacked for trying to cast, and with no CON and no Concentration, there's no guarantee that the spell won't fizzle. So you can basically only cast before stuff closes in to you. Between all this and the fact that casting occupies both twins' actions, I'm not at all convinced that your spells are going to be very useful to you. [–0.25]
Overall, I'm not getting a strong impression of what you do well. You've got high STR, Berserker Strength, and Power Attack, but you're way too squishy to survive going toe-to-toe for long against anything CR-appropriate, and Power Attack is your only real source of bonus damage (with a possible exception of Arcane Strike, but I'm not sure, because you didn't actually pick an 18th level feat; either way, there's a whole lot of levels before 18th), so you're not actually a good melee character. You've got some spells, but you lose so many caster levels that you basically never have level-appropriate ones, you can't cast them half the time, and casting spells ruins your dvati action advantage. You don't have enough skill bonuses to serve as the party skillmonkey. I just don't see a niche that you're able to competently fill.
Elegance: 0.75, raised to minimum of 1.0 Okay, first things first. Let's talk about your use of wildcards. This build, to be blunt, is not finished. It is not my job to assign your skill points for you. It is not my job to pick between Arcane Strike and Summon Elemental. It is not my job to figure out whether your familiar is a cat or a raven or a huitzl (all three of which are mentioned in the build table). It is your job to make those decisions and present me with a finished build. You don't get to rely on the judge picking the most favorable setup for you. That just plain isn't how Iron Chef works. Can you imagine one of the real (food-related) Iron Chefs presenting a judge with an unseasoned dish and a spice rack, telling them to add whatever spices they see fit? That's just as silly as what we've got here. I don't know what more to say than that. [–1]
You can't get 5 ranks in Heal by level 2. It's not a class skill for Wizard or for Barbarian, no matter how many variants you invoke. You can't actually get 5 ranks in Heal until you've got 7 HD, so even if you rejigger your skill points, that means that you're entering Flux Adept a level early. You can see that this puts me in a tough situation. There's no easy way to realign your levels to actually make this work, since you don't come anywhere near the CL 5 necessary to enter Blood Magus for quite a while. That's really not a good place to be. At best, that means that you're losing a level of Blood Magus (which means you don't get the Polyhaemia + Blood Draught trick); at worst, it means you're losing a level of Flux Adept (which still means you're losing the Blood Draught + Polyhaemia trick). Either of those costs you a level of spellcasting advancement, unless you put Wizard in the placeholder level. Plus it means you spent too many skill points. (You also spent too many skill points at level 5.) To be blunt, this is bad. [–0.5]
I'm not at all convinced that your "componentless spells" trick is enough to cast while raging. Even if we accept your dubious interpretation of False Theurgy (which, I will remind you, only works once per encounter, like all skill tricks do unless stated otherwise, and False Theurgy does not state otherwise), componentless spells still require concentration (they still take a standard action and still provoke AoOs without use of the Concentration skill, after all), and they still can't be cast while raging. Rage (or in your case, Berserker Strength, which has "the same limitation on actions as a barbarian in rage") doesn't interfere with components—it just says flat out that you can't cast spells. You will also notice that Rage specifically bans using metamagic feats, so even if we accept your dubious argument that you can use False Theurgy to mimic a Silent True Strike, you can't do that while raging, because you can't use Silent Spell while raging. Appealing to the GM's mercy because "you're using a FLUX ADEPT" might work in a home game, but this is Iron Chef, and we don't get convenient houserules to make things work the way we want them to work just because the RAW is inconvenient. The end result is that you've got a few levels where you just can't cast, and then you've got a bunch more levels where you can only cast until something hurts you, which doesn't seem like an effective way to play a character. (It's also a massive rules headache whether you can cast when one twin is Berserk and one twin is not, since both twins have to concentrate to cast a spell, but even glossing over that, this isn't pretty.) Overall, I just plain don't think it works. I respect the amount of effort you put into trying to make Barbarian play nice with Wizard casting, but ultimately, it doesn't actually do what you want it to do, and the entire character just suffers from a massive lack of cohesion as a result. [–1]
You also don't qualify for Blood Magus. When you take Blood Magus, you have 1 level in Wizard and 6 levels in Flux Adept, for a total of CL 4 on your Wizard casting. Blood Magus requires CL 5. You could fix this by swapping Flux Adept 7 one level earlier and putting Blood Magus one level later, but you didn't do that, so that's another way your build is illegal. [–0.25]
I do appreciate the use of Bear Totem Wasteland Barbarian to take care of many of the troublesome prereqs for Blood Magus and Flux Adept. Since Toughness, Great Fortitude, and Endurance aren't Fighter bonus feats, it's actually relatively tricky to get them all from class levels. The fact that Great Fortitude is a prereq for both Blood Magus and Flux Adept might be obvious, but I already dinged you for that in Originality, and I do like seeing prereqs serve double duty, so I can give you some credit for the nice way you handled those prereqs. [+0.5]
I've got you sitting at a total Elegance of 0.75 right now. The minimum score is 1, so we'll bump it up to 1, but there's really not much that's elegant about this character.
Use of Secret Ingredient: 1.5 The fact that you didn't finish the SI is unfortunate. Regeneration is an ability that's otherwise really hard to get as a PC, so passing up on that is definitely regrettable, especially on someone as squishy as you are.
Overall, I'm not sure what good Flux Adept is doing you. Deadly Spittle is a clever trick, but with only enough CON to get 3 (or maybe 4, depending on how you read "minimum 1") doses of it per day (and note that being a dvati doesn't let you double it—you get 3 per day, not 3 per day per body, so spitting from 2 bodies at once will just drain your reserves faster), I'm not really seeing it being a primary strategy for you. Feign Death might be useful for someone so squishy (and of course, that's a massive headache as far as dvati are concerned—can one Feign Death without the other one doing so?), but beyond that, I don't see you actually making much use of the abilities. I guess the fact that you actually like to make physical attacks makes Haste a little more useful for you than for your fellow chefs, though you seem to be under the mistaken impression that we're still using the 3.0 Haste that just grants an extra standard action, which isn't at all true. And I guess that you do have the (obvious, but still flavorful) trick of Blood Draught + Polyhaemia = "my blood is all the potions," though it's not clear to me if that's really going to matter by the very, very late point at which it comes online. (It's horribly unclear how either Blood Draught or Polyhaemia work with dvati, anyway; I'm inclined to think that at least Polyhaemia does care which twin drank the potion, though I could go either way for if Blood Draught cares which twin's blood holds the potion; either way, it's ugly.) Also, your Barbarian-ness actively interferes with using Polyhaemia; you can't make INT-based checks, including Craft: Alchemy checks, while raging, so I hope you aren't at low HP when the time comes to use Polyhaemia.
If you're relying on your familiar to make all your skill checks for you, remember that your familiar doesn't get the Flux Adept features that boost skills, so you're basically losing the SI's features there. Grace Through Will has no effect on whether "you can keep marbles from destroying your charges"; only true ranks in Balance prevent flat-footedness when Balancing, and since you didn't actually assign your skill points before plating up the dish, I have no idea when you actually get enough ranks in Balance to deal with that sort of thing.
Being a dvati doesn't actually help most of your Flux Adept abilities; on the contrary, it makes many of them less efficient. The dvati rules say "In most cases, an effect that applies to one twin fails to spill over to the other," so you have to burn more of your precious uses per day if you wanted to give both twins claws, or have both twins sweat acid, or have both twins use Haste, or have both twins use Pheromonic Control. It's not even at all clear how Polyhaemia would work for them (or for that matter, if Blood Draught is tracked for them separately); only Personal spells are automatically shared, and you can't even put a Personal spell in a potion, so it looks like you have to even track your potions separately. In short, being a dvati actively interferes with you getting a lot of use out of most of your Flux Adept abilities. That's kind of a big deal, and not in a good way. Honestly, I think that's your biggest problem as far as UoSI goes: many of the SI's abilities are use-limited per day, you don't have enough CON to use them very often, and you have to use them twice as often as a normal person to get the same effect, so you're really drastically limited in how much use you can get out of the SI's features.
I can see the effect that Flux Adept had on your build, in that it seems pretty clear to me that the prereqs pushed you in the direction of Barbarian. The downside is that I still don't see how Barbarian meshes with Flux Adept at all, so you just have this weird contraption of a character who doesn't seem to know what it wants to do. You're a Barbarian to facilitate Flux Adept, but you didn't do anything with Flux Adept once you got in, so you've just got this hodgepodge of abilities that don't really seem to make much sense.
Your one saving grace is that the character is chaotic enough (in terms of design, not in terms of alignment) that it's not automatically the case that you'd be stronger for being more of your base classes, but that's really just because your non-SI classes are all over the place and don't really do you much good. All told, though, you can't really benefit from the SI's abilities, so even though you were building toward the SI instead of building around the SI, you still don't really need to be a Flux Adept. [–1.5]
Final Thoughts: Playing a dvati is always kind of swinging for the fences. You know that they're pretty cheesy to begin with, so you're pretty much going big or going home. I can tell that you knew this, since you've got a hell of a lot of shenanigans packed into a single build. I do applaud your bravado; it takes guts to put a dish like this in front of the judges. Unfortunately, I'm not convinced that it actually works. I really have no idea why this character made any of the choices they did. Wizard and Barbarian are like oil and water here, and Flux Adept honestly comes out of nowhere, especially considering that dvati actively fights with it. Overall, no part of this build plays nicely with any other part of the build, and you end up with a character who doesn't really have any strengths. The only thing about this character that really impressed me was using Barbarian to take care of most of the annoying prereq feats for Blood Magus and Flux Adept, but beyond that, there just wasn't much to recommend it.
Total Score: 7.25
Originality: 2.5 Blood Magus. Yeah. I'm not just taking off points because there were three Blood Magi. I'm taking off points because there were three Blood Magi and Blood Magus was the very first thing I thought of when I read Polyhaemia. (Plus, the fact that it's got overlapping prereqs and offers Heal as a class skill makes it a pretty natural choice for Flux Adept.) So you've got the double whammy of it being obvious and it being repeated. [–0.5] Beyond that . . . you're a Wizard. You've got a touch of MotAO (but not enough for the full Spellpool), and of course you're a Flux Adept, but fundamentally, you're a Wizard. You're not the only Wizard (though you're the only Wizard who went for basically a full caster build), and you don't do much that differentiates you from any other Wizard/Flux Adept, so I'm not seeing anything that makes me want to give out extra Originality points.
Power: 4.0 You're the only chef to hit 8th level spells, which is worth something. You're not the only one to basically play a full caster, but still, you do have the highest level spells of anyone in the contest, so that's worth mentioning. Sure, those missing 5 levels definitely hurt at the end, but you pretty much brought about as much magic to the table as it's possible to bring without losing levels in Flux Adept, so you can get some points for that. [+0.5]
While your UoSI is likely not happy about the fact that you waited until the last possible minute to take Flux Adept, the fact that you took it so late does mean that you have as much spellcasting advancement as possible before you start losing caster levels, so you're able to pretty much function as a normal Wizard (minus a few annoying prereq feats) for the first half of your career, which is definitely helpful. I like seeing a strong early game, and with full Wizard casting, you definitely can solve problems early on. [+0.25]
I'm not sure if Focused Specialist helps you more than it hurts you. At high levels, most of your spells known appear to be Conjuration, but at lower levels (where you're more likely to need to worry about running out of slots in the first place), you almost seem to like Transmutation and Abjuration spells as much as Conjuration, and I wonder if you're actually going to have enough slots per day to do everything you want to do. Conjuration spells are powerful enough that you can probably find a way to muddle through with them, but it does make me wonder. I guess we'll call that even. 
Your feats are basically divided into two categories: Strong Wizard Feats and Annoying Prereqs. You do have a lot of annoying prereq feats (Cooperative Spell, Toughness, Great Fortitude, Endurance—Heighten Spell is kind of a mix of prereq and useful on a Wizard), but your non-prereq feats are all pretty useful, give or take Acidic Splatter (it's a nontrivial matter for a prepared caster to devote a high-level slot to powering a reserve feat, since that has a much higher opportunity cost than a spontaneous caster doing so; that said, it's not a bad option to fall back on, though I really would have ideally liked to see Precise Shot to make the RTAs easier). Collegiate Wizard is a great way for an Iron Chef Wizard to get lots of spells without quibbling over how much gold you have to spend and how many scrolls you can find, Practiced Spellcaster is good for shoring up the weaknesses of the SI, Craft Contingent Spell is crazy powerful, and Minor Shapeshift is good for any caster who has the feat space available. With three PrCs, each of which requiring at least a feat or two that you wouldn't take on your own, you've got a lot of prereqs to burn through, but your non-prereq feats definitely stand on their own merit. I'm almost hesitant to give you more points for them, though; I've already given you points that boil down to "you're a Wizard, and Wizards are powerful," so rewarding you for taking powerful Wizard feats like Craft Contingent Spell and Minor Shapeshift kind of feels like letting you double-dip in "Wizards are powerful and have powerful toys." (There's also the not-so-minor problem about you taking feats that aren't legal bonus feats, meaning that you'd actually have to give up some of your powerful feats to make the build legal, but we'll talk about that in Elegance.) So I guess I can give you a little more credit here, but you've already earned the bulk of what I'm giving you. [+0.25]
Elegance: 2.0 First off, Toughness isn't a Fighter bonus feat, so you can't get it instead of Scribe Scroll. Weird, right? But them's the rules. Believe it or not, Great Fortitude isn't a Fighter bonus feat either, so that's also not a legal bonus feat for you. In Iron Chef, always, always, always check the prereqs for your feats, and always, always, always check your bonus feats to make sure that they're legal choices. You aren't the first person who's been burned by this, and you won't be the last. But the fact remains that you don't qualify for the SI, nor do you qualify for Blood Magus. None of your other feats are Fighter bonus feats, so you can't just shuffle things around and become legal. That's bad. Very bad. You'd have to radically redo your feats to make this legal, probably losing Collegiate Wizard and Acidic Splatter (though you could conceivably shunt Heighten Spell up to 3rd level and then Cooperative Spell up to 5th level, since you can take a metamagic feat as a non-Martial Wizard bonus feat, so you actually might be able to keep one or the other of Collegiate Wizard or Acidic Splatter). Honestly, I'm tempted to slap you with a Failure To Qualify, since the build is flat out not legal as presented, it takes more than trivial changes to make it legal, and one of the things for which you fail to qualify is the Secret Ingredient. Since you could theoretically make it work by losing one of your feats, I'll just assess a half-point penalty for each illegally chosen feat instead of giving you a zero for FTQ, but you really need to be more careful about that. [–1]
You overspent a skill point at level 11, since Concentration is cross-class for the SI. You accounted for that at every level of Flux Adept after that, but you did mess up there. A minor problem, but still a problem. [–0.25]
I dinged you in Originality for taking Blood Magus, but you definitely took it for the right reasons: Blood Draught + Polyhaemia is highly flavorful, there's that overlapping Great Fortitude prereq, and perhaps most importantly, it gets you Heal as a class skill without losing any caster levels. It's unfortunate that you still didn't get into Flux Adept any quicker than you would have by just taking Heal cross-class, but still, you definitely paid attention to your prereqs, so that's nice to see. [+0.25]
I do not believe that you get access to Bard and Sorcerer spells by means of the Spellpool. The sidebar on pg. 49 of Complete Arcane is very clear that the Spellpool has spells "on the wizard/sorcerer spell list in the Player's Handbook," which is not the same thing as Bard spells (or non-PHB Sorc-only spells). The Spellpool is still a useful trick to have, but you're still just a Wizard, not a Wizard with Bard spells. 
I definitely like seeing Quick Potion. I actually really like that spell, since I think potions are thematically very cool, and Quick Potion is a great way of making them not be a major gold drain. The downside, of course, is that you only have access to Polyhaemia for all of two whole levels (at an ECL where having access to a couple extra 2nd- and 3rd-level spells per day really doesn't mean jack, especially when those extra spells are subject to the limitations and downsides of potions), so that's regrettable, but I do like seeing Quick Potion as a way of enabling Polyhaemia. It's not useless before Polyhaemia, of course, but it's not so powerful that it's worth a bump in score anywhere. Still, I wanted to mention it. 
Use of Secret Ingredient: 1.75 The fact that you waited until the last possible minute to enter the SI really makes me think that you were avoiding it. And to be honest, you didn't do anything with the SI that actually makes sense for the character. You have a much higher Bluff than the average Wizard (between having it as a class skill, Pheromonic Control, and Taste of Truth), but you didn't tell me why you really care about that, and with no other face skills, it's kind of weird to have someone who can lie like a champ but who can't convince anyone of anything honestly. Polyhaemia is thematically appropriate (especially with Blood Draught). Other than that? You seem to mostly just care about being a Wizard, and Flux Adept makes you a worse Wizard, which really doesn't do anything to convince me that Flux Adept is a natural choice for the character. This is compounded by the fact that the Flux Adept abilities that you get the most use out of (Taste of Truth, Polyhaemia, and Regeneration) all come super late in the build, so there's a lot of levels there where you're really just strictly worse for having Flux Adept and don't really have much to show for it.
Overall, this is an obvious case of a build who took the SI because it was the SI, not because you liked the abilities or because it was a natural choice for you. All of the SI's abilities seem like things you rationalized after the fact instead of things you actively incorporated into your build. Pretty much anything you can do is done despite being a Flux Adept, not because of it. You did take all ten levels, and you did put some token investment into Polyhaemia and Taste of Truth, but beyond that, I just don't think you actually used the Secret Ingredient well. [–1.25]
Final Thoughts: Fundamentally, you're a Wizard,
Harry Liana. Your Power benefited from basically being a full Wizard, and your UoSI suffered for the same reason, since your Wizardliness totally eclipsed anything you got from Flux Adept. You definitely got too clever with your bonus feats; always double-check your feat prereqs and your bonus feat options. Vizzini was either too strong or not nearly strong enough, depending on how you look at it; either way, Blood Magus was an obvious and thematic choice, but it suffered from being too obvious. At the end of the day, this is a perfectly strong character, but it's an unremarkable Flux Adept.
Total Score: 10.25