Some webmasters suggest a workaround using an audio recorder like Audacity for that purpose and while that is one possibility it is not the most comfortable one.

SWF Rip is an Open Source software program that serves the purpose of extracting objects of swf files to the computer. The software has not been updated for some years but it still works surprisingly well on most swf files. There might be some that it is not working with though.

All that needs to be done to extract the contents of the swf file is to open it in SWF Rip. The program will display the contents sorted by type like sound, image or sprite.

A right-click on a type or single object provides the means to save all or only the selected objects from the swf files. This obviously includes the possibility to extract all mp3 files from the swf file. There is also the possibility to save all objects at once.