Here's a note from After Effects Help that gives a brief list of limitations of SWF import:
SWF (continuously rasterized)
It's that last sentence that is directly relevant here.
There's more about working with Flash and After Effects here.
What Todd said... If this is a regular workflow for you, you should author your flash content in such a fashion that the nested clips are dynamically loaded external SWFs by thmeselves. This would allow you to import them separately in AE... Otehr than that you may also consider Flash Catalyst for doing specific animations. It is kinda like AE with its timeline, but can handle Flash stuff fully...