Your request will have perhaps two answers.
I was wondering if I can have a fancy looking flash player to play m3u files for my website
Yes, you could have a fancy Flash player play the audio files (probably mp3s) that the m3u files point to. The m3u is just the playlist and not the actual audio file. The second part is from the title of your post
As mentioned above, probably lots out there.
A Flash audio player can be created to look like anything you want. A guitar:
or a gramophone:
or anything you may envision. The playing action is all in the invisible ActionScript.
These examples use an xml playlist instead of the m3u playlist so some adaptation may be needed if you want to do your own custom creation.
Looks like you have or work for a Web Design company. Perhaps learning to create your own custom players would be a good way for you to promote your business.
the same is true for custom Flash video players:
Here’s a source for good tutorials:
Eye for Video