With the help of my sister, I came across this awesome online application for converting YouTube flash video to MP3 audio. This service is fast, free, and requires no signup. All you need is a YouTube URL, and their software will transfer the video to their server, extract the MP3, and then will give you a link to download the audio file.
Head on over to: http://www.listentoyoutube.com/ to give it a whurl.
Make sure that your aware of their terms before using this service.