I have done a lot of conversion from .swf files. They can be really tricky to mess with or really easy depending on how they were built. If it contains one complete audio file (e.g. song) then its easy, but if there are lots of separate little audio segments in .swf then often times, the conversion goes out of sync. I use ADShareit as a first attempt to convert the files. I have found it to be the best out there. If I still get audio sync issues, I usually just do a screen capture. set the flash up to about the correct dimensions, and record it. I like Camtasia Studio for this. Another thing that can get tricky is if there is user interaction in the .swf file. Its best to practice just how you want it to go, and then use a screen recorder.

This is all for flash files (swf) which mostly store the images as vectors (thats why they can be scaled up very nicely), however if you have flash video (flv) thats a whole other story. You just convert it like it was any other video.