Exported MOV from Flash Pro with alpha channel doesn't retain transparency
Seeing as this appears to be a bug, my only suggestion is to export it as a PNG sequence. At my work we always transfer from Flash to AE as a PNG sequence, as we find MOV notoriously unreliable and buggy. 

If you need to retain an audio track, try exporting that separately as a WAV or MP3 and placing it on your timeline in AE.