We posted about X2X, which is a free app to extract audio files from almost any Video file, here is another app on same lines. FLV Extract is a dedicated app which allows you to extract audio (MP3) from FLV files.
FLV Extract is a small application to extract Audio, Video and Timecodes from a media files. Once downloaded, extract the zip file and run the executable file.
Now choose what is to be extracted, and later simply drag and drop the FLV file to get the new files in same folder. You can either choose to extract audio as an MP3 file or just the video without any audio in it.
It supports AVI (H.263/FLV1 and VP6/VP6F) or raw elementary stream (H.264/AVC). The audio is saved as MP3, AAC (with ADTS headers), Speex, or WAV (PCM). Recently updated for .Net Framework 4.0.
If your requirements are beyond FLV to MP3, then you will have to search for some other application.