I would start with it in one place and work out the leg and wing motions first. The parrot would need to launch off it's perch so I'd start with the legs and wings during the launch. I imagine it would squat down to prepare to jump up and start extending it's wings as it did so (although I'm no expert on bird movements so I'm just guessing). Once it got it's wings extended and it's body is in a flying pose, I'd do one cycle of the flapping and tweak that until I got it as smoothly as I desired. Then I'd copy and paste the keyframes repeatedly along the timeline so the wings would continue to flap repeatedly. Once the wings were moving as desired, then, and only then would I move the parrot around on the screen. By doing it like this, I can move the cameras as much as I need to see the take off and flapping and then move them back into place to work out the full scene - in other words I'm focused on only one aspect of the animation at a time.

Before they made me they broke the mold!
http://home.roadrunner.com/~kflach/