Would a small bird with wings in a cage in the space shuttle or ISS be able to fly with the low gravity of the

space shuttle or ISS

ISS = International space station

Probably not at first, as the wings would generate too much lift since the bird is used to 1g.
After some time, the bird will adapt, open it's wings less or beat them much slower.
Bird flight has already been tested in the "vomit comet" See the youtube clip below.
Note that the birds are generating too much lift, You can see this in the slow motion part,

Insects cope better as the air appears viscous to them so gravity is not as significant.

The second clip is some weightless cats for your amusement

Yes and no... The bird would probably have an easier time moving around in 0 or lower gravity environments over humans.. The bird could propel its self with just it's sings wear as a human needs to push off of something.

A bird flys by moving air around its wings.... Which is still possible in the space shuttle..

The potential problems I see are that birds are used to gravity and they do use it to some extent when they fly.. Diving and what not..

The other potential problem I see is that I do not know if birds are intelligent enough to figure out how to adapt to the low or 0 g..

But for the most part the general mechanics of flight are the same..

Why would you assume they could not?

The viscosity of the air would remain essentially the same.
The only major issue is the lack of noticeable gravity.

Humans can handle it well enough.
Bees, flies and other flying insects have handled it well enough during previous experiments.

Why would a bird be different?

I thought they tried this and discovered that the birds quickly glided instead of flapped. Maybe it was insects.

I'd have to ask why would it need to when it can float?