I've been having trouble using the Flash player in Chrome for a while. It kept trying to play everything in a VLC plugin. So, I've took the cheap path and just started using Firefox instead. Today, I started running into the same issue.
To get it to stop trying to use VLC, I went into Apps in Firefox and set all the of the media types that were using VLC to use ask me, instead. There wasn't any option for Flash. The immediate result is that it tried to down load anything I tried to play as a local M3U file. There were some apps in the dialog I could use, instead, but none were in the browser.
Did the same thing in Chrome. Disabled the VLC plugin. Again, now I'm simply prompted to download the play list.
I can still access my Subsonic server just fine with other applications, and even in a browser (with Jamstache), but not with the integrated Flash player.
This sounds like a browser issue, not a Subsonic issue, but I'm out of ideas on how to make the browser use flash to play music in the Subsonic GUI. Anyone else have any ideas?