Did you create this file yourself or is it some type of template?
If it's using a FLVPlayback component, then you don't want to "export" anything, you simple "Publish" or "Test" (Control/Enter) to produce a .swf.
This is the player for the video file. And I'm just assuming that the movie clip is to hold the various animations that are triggered by the cue points?
So you would have your main "Player" .swf file, an external actual .flv video file, plus a number of other external movie clip animations that get loaded in as the cue points call for them.
So I don't see why you would be exporting anything, just Publish the .swf.
I created the .fla myself, it is not a template. The resuultant SWF is perfect for upload to a website - which was the original brief. However the client has now also requested a .mov format for other additional uses, including upload to youtube. Is this possible with the setup I have ?
Not really, at least as you currently are attempting.
The resulting .swf works well because it's bringing in those external assets, the .flv and animations at runtime and these are not included if you "export" as .mov.
Perhaps the easiest way to accomplish is to run the .swf on your desktop and use a screen capture to record the entire sequence. Then save that file in whatever format you like.
Use something like Camtasia