MP3 support in Firefox has even already landed for Windows 7 & 8 in Firefox 21, see:
Mozilla is currently working on support for Linux and OS X too. Unfortunately they need to use the operating system codecs rather than implementing it directly, due to the patent issues that H.264 and MP3 have (WebM and Ogg Vorbis would have been the better choices, but the better choice often loses in such battles, unfortunately).
I am writing this with Firefox 21 on Windows 7 with Flash disabled, but audio doesn't work here. Give it a try yourself: http://www.mozilla.org/en-US/firefox/channel/#aurora
IMO it should really be the other way around. HTML5 audio (& video) should be the default, and Flash the fallback if HTML5 audio/video is not available. The Modernizr JS library can help to query for which formats are supported, in case you want to use MP3 only for HTML5 audio with Flash fallback. Which is only the 2nd best solution (best would be MP3 & Ogg Vorbis of course), but still better than Flash only or Flash as primary source.
I haven't explored Rocket Record yet, so can't say much about this feature. But for video and audio I don't see much reason why to wait any longer.