$ vlc -I dummy -vvv "Myvideo.flv" \
--no-sout-video \
--sout-audio \
--sout="#transcode{acodec=mp3}:std{access=file,mux=raw,dst=myaudio.mp3}"

-I dummy = dummy interface (do not use GUI)
-vvv = some verbousness doesn't go bad
myaudio.mp3 is the destination file
std = abbreviation of "standard". This module saves the stream to a file or sends it over a network, after having muxed it.

More info on module chain load on http://www.videolan.org/doc/streaming-howto/en/ch03.html