Why is Coco flapping his wings so much? It's so weird how he does it for a continuous minute. But when i try to record him, he stops. I've only gotten a few seconds of video, but the tiny amount of flapping done on-camera is a lot more while off-camera.

Why could he be doing this?

Lucy does it too. I think they're just exercising their wings.

Lucy likes to lean forward, as she flaps her wings. Sometimes, she just simple spreads them (probably for the sake of stretching), and almost hangs upside down.

He's exercising. It's perfectly normal and healthy for birds to exercise their wings on a perch. It's basically flying in place. Why he stops when you try to take a video? It's because he is more interested in your camera then flapping his wings.

Or he is either frightened by the camera or he doesn't like to be watched. I remember when I first had only Beaker, he would try to practice talking only when I left the room. When I came back, he hide everything he did.

Not liking being watched sounds more appropriate. Lucy will flap her wings, and if I do so much as look at her, she'll instantly stop.

That's just what Coco does!

My cat is like that. He has a toy that is a ball that runs around a track in a circle. He can make it go so fast. But, if he catches me watching he stops. I think he gets embarrassed.