English Translation
The birds flap their wings while flying.
Apparently for birds the best translation is batir las alas. Agitar is movement of the arms of a person. Should be changed
Just to add on it, because I find the idea funny: I agree that “batir” is a better translation when they are flapping to fly, but they can also “agitar” their wings (for example, when pigeons move out of your way, and start opening the wings, and moving them a bit, but end up just running and not flying away). The sentence “Los pájaros agitan sus alas mientras vuelan.” seems to imply that they wing movement and the flying are not related, and what comes to mind is the bird flying while doing just random wing movements, and yet proceed with its trajectory as if everything was ok : D