Since the release of Flash CS3, a new feature called QuickTime export was introduced.  QuickTime export allows you to export Actionscript driven or timeline animations into a QuickTime movie file.  One key advantage of exporting Flash as a QuickTime movie is the ability to playback your heavy animations as fluid as possible with no skipped frames.  

Lee Brimelow walks you through the process of exporting ActionScript-based animations into a QuickTime movie and then compositing it within After Effects.  In the process of demonstrating this feature, Lee also gives some additional advice with ActionScript-based animations.