$ mplayer -dumpaudio input_file.flv -dumpfile output_file
...was giving me a binary file that I couldn't use.
After some Googling, reading and trying I found this worked:
$ mplayer -ao pcm:file=output_filename.wav -vo null -vc dummy input_filename.flv
The output file from an 8MB flv was a 50MB wav file.
To get it in a smaller file I converted it to an ogg:
$ oggenc output_filename.wav -o target_filename.ogg
The resulting ogg file was 3.7MB
I got help from here: http://linuxgazette.net/131/howell1.html