How to deal with a Monk wyrmling?

[Mrark]

Hi everyone. I'm running a campaign and we are getting to pretty high levels. I am a wizard 5, incantatar10 and archmage 2, and I have been having a wyrmling two headed dragon since the the lowest levels. Now, my DM allowed me to advance the dragon with class levels, and I asked the monk in my group to train him. So now he is Monk1, and soon to be monk 2. I am asking how it can work mechanically. I mean, how do we treat his natural weapons with the monk feats? Do they get buffed somehow? How should a flurry of blows work?
Even some reasonable Houserules are accepted as solutions. I am not just asking for RAW, i also want to know your opinions.
Let's say both :D

[Biffoniacus_Furiou]

He can full attack with unarmed strikes, including iterative attacks, and use all of his natural weapons to make secondary attacks.

His natural weapons aren't special monk weapons, so he can't use both flurry of blows and make secondary natural attacks on the same full attack. I recommend trading flurry for an alternate class feature.

His natural weapons are going to do their normal damage, secondary attacks are made at a -5 to hit (-2 with Multiattack) and add half its strength bonus to damage (except the tail slap, which adds 1.5x str to damage (https://www.d20srd.org/srd/monsters/dragonTrue.htm), if it has that).

[Gruftzwerg]

As Biffoniacus_Furiou said.

Other option would be to take Beast Strike and add your claw dmg to your unarmed strikes. If you don't use any other natural attacks, you can flurry with Beast Strike.