IIRC, Flash is not required, but provides a fallback for those browsers and devices that do not fully support HTML5 audio.
It links to a sound file-format test, where I see Firefox plays only ogg and wav. That made me wonder if one could do mp3 decoding on the browser. It's possible: http://labs.official.fm/codecs/ but it sounds totally broken on Firefox on my Ubuntu.
So no Flashless SoundCloud on my Firefox yet, but it may soon change: https://bugzilla.mozilla.org/show_bug.cgi?id=799318
Every html5 audio test I've found worked just fine. Except for Apple's, because it, similary to soundcloud, sniffs user-agent to serve different version of a site.