Other than the sheer absurdity of it (read: real world limitations), is there anything stopping a multiclass Monk/Druid from using flurry of blows while in wild-shape?
First, let's look at Flurry of Blows:
The Feral Combat Training feat will add a natural weapon to the monk weapon lists.
However. Tigers, as any other creatures, possess an Unarmed Strike. This means your Improved Unarmed Strike is relevant, and everything under "Unarmed Strike" in the monk description is relevant too. Including and especially:
So even though you have natural weapons, you can decide not to use them and do a normal Flurry of Blows, dealing damage as shown under "Unarmed Damage" (using your modified size).
So yes, a tiger can do kung-fu (a T-Rex too).
You cannot usually use natural weapons as part of a flurry of blows, so by default the answer is no. Luckily Paizo has come to your tiger-monk's rescue with the Feral Combat Training feat in Ultimate Combat, which explicitly allows this. See Can I use a full attack and natural attacks in the same round? for how natural attacks and monk flurries interact usually.