There is another alternative if you're using a professional edition of the flash IDE. Pro versions of Flash ship with the 'Flash Video Encoder', this can be used to convert various video formats to .flv.
It doesn't support directly converting .swf to .flv, but there is a workaround:
1. Open up your .fla in the flash IDE and export your .swf as a movie in .mov or .avi format ( select 'File->Export->Export Movie' in the menu or press ctrl+alt+shift+S )
2. Enqueue the exported movie (.avi or .mov) in the video encoder and convert it to .flv
As already mentioned, you can only do this if you've got a professional edition of the Flash IDE and the 'Flash Video Encoder' installed.