Thank you a lot, Vince. I realize now that my question belongs in a Flash forum and not After Effects. Though your instructions didn’t work for me, they inspired me to keep looking through the various choices and settings, and finally I did something that resulted in a QuickTime movie with content in it.
(Apparently the FLV file was problematic for importing in the way you suggested because it had an audio codec that couldn’t be imported, so though the warning suggested that video would come through (all I wanted anyway), nothing ended up on the stage. The Load External Video with Playback Component in Import>Import Video worked, though, at least to the point where publishing a Flash preview worked; and then exporting to QuickTime did nothing until I figured out that I had to check “stop exporting after…” and fill in the exact time of the clip. Now I have a working QuickTime movie and I’m sure After Effects won’t have any problem with it.