what reasons have we to believe that dinosaurs with wings could fly?
I think the simple answer is that feathered dinos used their feathers for insulation (such as Bamiraptor or velociraptor), rather than flight (the feathers were symmetrical).
They also show a half moon wrist bone (for grabbing) that could have allowed for a powerful down stroke of the arms: but do these count as wings? Certainly not capable of powered flight.
Feathers at this time (approx 135-65 mya) were mostly symmetrical so they could not really generate lift (see Caudipteryx).
Archaeopteryx, on the other hand had overlapping asymmetrical feathers but a pretty small breast bone compared with modern birds so it would have fluttered alone (rather than gracefully flying) and these were about in Jurassic times.
So I think you would be hard pressed to find an non avian flying dinosaur (to the best of my limited knowledge).
The kind of evidence we would need, I suppose, would be of such creatures living in high places that would not be easily reached by non-flying creatures.
Your best bet would be to look for a non avian feathered dinosaur fossilised in flight, at altitude. That would be a smoking gun.
Edited by Larni, : No reason given.