The only other widely available frameworks that have audio capability that I know of are silverlight and unity, but I doubt those are supported on Raspberry Pie and are probably just as heavy as flash.
I think your best course of action is to research why HTML5 audio might not be working, or build a native application.
Usually web applications like Pandora instead offer a native application on the mobile device instead of trying to get the website to work, since they would have the same challenges you do for getting a website to play audio.