A monk multiclass options

[Sir cryosin]

I'm playing a kobold shadow monk. I'm thinking of taking a 3 lv fighter dip. For maneuvers, action surge. But I'm lost on fighting style maybe I'll ask my DM if I can use the protection style with out the shield requirement.

[Arcangel4774]

If you're not dead set on fighter and maneuvers, maybe consider the easy 2 lock dip for reliable range damage and devil sight so you can see with the darkness spell

[Toadkiller]

Because it's not called "5e" anymore. It's called "take some levels of _____lock".

[djreynolds]

Shadow step at 6th level is awesome. 2 levels of ranger would fit nicely with archery style to go along with your high dexterity. Archery's range will expand your monk's range tremendously. You can punch some one, shadow step, and then launch an arrow. And it will get hunter's mark, it lasts 1 hour. A 3rd level will get you hunter and you could grab horde breaker for a free punch.

[Crgaston]

Well, the obvious choice is Dueling. +2 damage to your monk weapon with a free hand for martial arts. But rather than maneuvers, a fighter 1/rogue 1 or 2 might do more for a monk than a straight fighter 3.
Archery is also a strong contender for better ranged attacks, something the monk lacks.

[Malifice]

I'm playing a kobold shadow monk. I'm thinking of taking a 3 lv fighter dip. For maneuvers, action surge. But I'm lost on fighting style maybe I'll ask my DM if I can use the protection style with out the shield requirement.

Mariner if UA is allowed. Duelling is OK to add a bit of extra damage at higher levels once your MA dice is a d6 or better. Archery gives you some good ranged options when you can get close enough to face punch (and flying targets).

[MeeposFire]

Go with mariner if you are allowed it works unarmored (and gives a swim speed which is fun for a monk).

If that is not allowed do not take protection even if the DM allows it to work without a shield unless the DM also just makes it easier to use in general. There are so many restrictions on that ability that you will be hard pressed to use it and for a monk the biggest one is being next to people. As a monk you generally are going to use your mobility to get to isolated targets to take them out. You generally do not stick around your friends as much as a fighter might. If you have a party with lots of people that may actually stay close to you then it might be slightly better but even then the other restrictions will rear their heads and prevent you from getting the benefits you really want.

Best option PHB only is either dueling for extra damage (though it only applies to your attack action attacks with your weapon) or archery which does not make you better at what you normally do but it does make you better at range which is normally a monk weak spot to a degree.

[Sir cryosin]

Warlock is off the table because
1. There is no warlocks in this campaign( it a avatar the last Airbender game.)
2. My charisma is 9
My shadow muck is a chi blocker

[Citan]

I'm playing a kobold shadow monk. I'm thinking of taking a 3 lv fighter dip. For maneuvers, action surge. But I'm lost on fighting style maybe I'll ask my DM if I can use the protection style with out the shield requirement.
Hi!
Take Mariner if allowed. While some of the benefit overlap with Monk 9, it's still a solid choice.
Otherwise, Dueling.

[Specter]

Rogue is very nice too. Expertise in Stealth, sneak damage and cunning action sell the whole package. You could ask your dm to approve the Mariner FS if you're going Fighter.

[odigity]

If you're not dead set on fighter and maneuvers, maybe consider the easy 2 lock dip for reliable range damage and devil sight so you can see with the darkness spell

It's not reliable if you can't hit, which you won't, since you can't pump Cha on top of Dex/Con/Wis.

[SillyPopeNachos]

Rogue is very nice too. Expertise in Stealth, sneak damage and cunning action sell the whole package. You could ask your dm to approve the Mariner FS if you're going Fighter.
Rogue, Ranger, Fighter, and Druid are all solid considerations for any monk, but for a shadow monk rogue is supurb.