flash video (flv) being a proprietary format, i doubt there’s any freeware programs out there (i’m possibly wrong though as i haven’t sifted through the mountains of google hits - perhaps you’ll find what you want if you’re patient enough to look through the searches)
anyhow the alternate method i was thinking of is to use a screen capture software (for example camstudio which is freeware), play your flash animation and capture it, then upload the captured video to youtube which will encode the flv for you for free (and obviously redownload it back from youtube). when capturing, try using a lossless codec for best results, but upload using a codec youtube can decode. 
I have a lot of .swf videos and I need to convert them to flash videos, I google search and find this software: Moyea SWF4Tutbe Converter - http://www.flash-video-mx.com/swf4tube-converter/
The program works very well, can fully all my .swf files to flash videos, but it is a shareware. So if anyone know a freeware can do this, I’ll be thankful to you for it.