So here's an idea:
Monk / Sorcerer / Dragon Disciple
Takes Weapon Focus & Feral Combat Training (bite), Dragon Style, Dragon Ferocity
Flurry with any combination of: Arcane Strike, Power Attack (furious focus), 2H Temple Sword // Bite (+stunning fist?). Gains Dragon Style damage bonuses on bite attacks from disciple bite or dragon form.
Seems to me like it should work unless I'm missing something, but is it cheap/cheesy?
Well, whether or not it works depends on if you're using Paizo's new clarification that says Flurry = Two-Weapon Fighting. Since you only have a single bite attack you'd have to combine it with another weapon. That means you can't flurry with a single two-handed weapon either.
A claw flurry would work though. Also, if you're just planning to ignore this clarification until Paizo says more since it breaks at least one monk archetype, then the bite flurry will work.
The general plan would be attacking with two hands on the sword while throwing one kick/bite in there, and making single attacks with either.
I thought that at the least you could put two hands on a weapon if alternating with another 'weapon' like a kick... but yeah, if you take their "clarification" very seriously it breaks or contradicts an awful lot - not least of which is using Feral Combat Training to flurry attack.
Claws are another option, but its two more feats to 'train' them, they're weaker than the bite, and it gets complicated if you're theoretically having to put away a weapon to use them.