You can use a Free FLV youtube video downloader when downloading a FLV video online.
http://download.cnet.com/Free-YouTube-Video-Downloader/3000-12512_4-10904885.html
Next,if you wanna convert FLV videos,you can select this video converter. It boasts superior quality and fast speed. In terms of its converting functions,it can convert formats including Flash Video/ YouTube video (*.flv, *.f4v), HD Video (*.tod, *.mod, *.m2t, *.m2ts, *.ts, *.tp, *.evo, *.mkv, *.dv ), General Video (AVI, MPEG, WAV, etc).
What's more,it enables users to edit videos freely such as triming,croping,screenshots. It also supports image formats like*.jpg, *.ico, *.bmp, *.png, *.gif, *.tiff.
The last but not the least,it completely eliminates out of AV sync issue 'cause it adopted advanced AV sync technology.
For more info,you can link:
http://www.pavtube.com/video-converter-mac/