IMHO Flux stores are not incompatibles with Backbone models / collections.
You can probably use Backbone collections as Flux stores, as long as you integrate them with the Flux dispatcher and you permit them to emit an event to trigger a rendering.
I'm just not sure Backbone models are meant to be immutable data structures in the first place, thus making it harder for React to optimize the rendering.
I would also say that I never really found all these Backbone models/collections methods really useful. In a Flux architecture, API requests would tend to be fired by action creators and not by the stores directly, thus permitting multiple stores to listen to the same request completion.
Where should ajax request be made in Flux app?