You can use ffmpeg to convert to WebM. Make sure to compile it with the --enable-libvpx and --enable-libvorbis flags (see FFmpeg compile guides), or visit the FFmpeg Download page for links to builds that include support. After that, you can use the following command (I’m using input.flv as my example input file):
ffmpeg -i input.flv -vcodec libvpx -acodec libvorbis output.webm
For additional information, see the FFmpeg vpx (WebM) Encoding Guide.