Long description, no real info. Sorry to be so harsh, but you're leaving out all the important parts like what versions of the programs, what system, what framerates, what makes up the layers in your SWF, what your SWF export settings are, whether there is audio involved anywhere and all those other annoying little details....
It's Adobe Flash Pro CS6, After Effects CS6. They're on mac os X.
Frame rates 24fps, both in Flash and AE.
All vector shapes created in Flash, in JPEG and PNG images. No nested symbols.
SWF file is created by Cmd+Return keys...No audio.
AE composition is 1920x1080(1.0).
Mmh, sounds so far bog standard stuff. Do any of your images have anything odd going with color profiles? Flash would just ignore them, but AE may somehow see that information. Also are there things like Flash's belnding modes or live layer styles involved? This might cause issues in an environment without hardware acceleration...