Step 1: Free download FLV to MP3 Converter and install it.
The interface is like the following:

Condition1: you already have flv video files on your computer.
1. Click file button, choose the flv video you want to convert
2. In output format, Choose MP3 (Audio only).
3. Click start convert FLV to MP3.
Condition2: Want to directly convert FLV to MP3 online.
Here we take youtube for example, if you want to convert FLV from youtube to MP3, it is very simply.
1. Click URL Button, copy the url to this FLV to MP3 to Converter, for example: copy the url
http://www.youtube.com/watch?v=Xz3CkM0QdK4&feature=dir
2. In output format, Choose MP3 (Audio only).
3. Click Converte to start convert FLV to MP3. For More Information See this Guide: How to download youtube videos
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