Is there a media-handling module that can handle midi files?
MIDI files can be embedded straight into the page with the &lt;object&gt; tag, so there should be some way to then output that with the link that views gives you at the moment. If you went with a separate field then it's be easy enough to do with Views output rewriting.

After a quick look for a flash solution, it seems that flash itself doesn't have any support for MIDI, so a flash based player is unlikely.