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Well, I've never have to deal with flv when extracting soundtracks, so I know only how to do the job with a video file ):
I would do it so - first convert flash to video, using any convertor, then...

I've never heard about SnagIt... as for Camtasia, it works fine, but is too pricy :(
My job involves creating tutorials, and I prefer Screen VidShot by geovid, which is a good combination of price...