I tried a quick search but didn't find any clarity of this.
Flurry of Blows states you take 2 unarmed Strikes
Dragon Stance states you can make dragon tail attacks that have the backswing, nonlethal and unarmed traits
Tiger Stance states you can make tiger claw attacks that have the agile, finesse, nonlethal, and unarmed traits
Forgive me for not quoting the complete listing of each of these, but as I read them it does not sound like you can use these "Stance Attacks" with Flurry of Blows because, even though they have the unarmed trait, they are not actually Strikes and are specific named attacks.
Am I just overthinking this?
Whenever an ability references one of the basic actions, it is that action for all purposes as far as I can tell. Flurry of blows gives you two strike actions for the price of one. While strike actions normally let you use either a weapon or an unarmed attack, flurry of blows restricts you to an unarmed attack. Crane Wing stance restricts all your strike actions to crane wing attacks which are unarmed attacks.
The two abilities work together perfectly. You would need to end the stance to shoot a bow since that requires a strike action and you are only allowed crane wing strikes while in stance.
It's probably best to think of the various style strikes as weapons.
My question would be. We already statued that crane stance work just fine with flurry of blows. Those that mean if you take the stunning fist feat it stack with those.
Meaning if any of the crane wings attack touch you get a chance to stun and it doesn't end your stance since it's doesn't have the attack trait. You don't break the only crane wing's attack.