This method will allow you to convert .flv video (flash) to mp3. In fact, this method can be use to convert almost any video (avi, wmv, mpg, rm, mp4, mkv, etc) to mp3. We will do it the easy, free and open source way.

MediaCoder is a free universal batch media transcoder, which nicely integrates most popular audio/video codecs and tools into an all-in-one solution.

First, download, install and run MediaCoder.

(1) Select the output folder where you want to save the encoded mp3 files.
(2) Click and drag the .flv files (or any otehr video files). You can drag as many video files as you want.
(3) In the Audio tab, choose LAME MP3 for the Encoder.
(4) Usually, I use Averate Bitrate (ABR) for Rate Mode. Set Algorithm Quality to Best Quality (0, you can drag the slider to the left). As for Bitrate/Quality, I would normally use 128kbps if I my source came from .flv files. The audio quality from .flv files are not very good, so 128kbps is sufficient. You might want to use higher bitrate (192kbps) if you are encoding from high quality source (x264 videos).

(5) Click the Video tab.
(6) Untick Enable Video
(7) You are ready to go! Press Start to begin the encoding process.

Encoding in progress

Finished!

[Mediacoder]

See also:
Easily Download Flash Video From Websites