if you're exporting a swf from ae, you shouldn't be importing it into flash. if you're exporting an flv/f4v from ae, you shouldn't import it either but you may click file/import and not actually be importing it.
which file type is being exported from ae?
Yes, you are right: the filetype that's being exported from ae is .xfl. Is this the correct file type for exporting to Flash??
This file I can import in Flash and in Flash it looks ok, but when I export the fla in Flash, the video isn't playing like it should (slower and not smooth).
Could be a mismatch of frame rates. For example, if you are using 30 fps in AE and 24 in Flash, and then you embed the video into the time line, it will play at 24 fps, slow and jerky.
However if the video file was a .flv and you played the video by NetStream or FLVPlayback, it would playback at 30 fps, even if the Flash doc had a fps of 24.
If that doesn't fix it, try exporting the file from AE as an flv.
an xfl file is the xml form of an fla file. you could open (file/open) that with flash cs5 and then publish (file/publish) a swf and you can save (file/save) an fla file.
what exactly are you doing?