Unfortunately MSE support is not complete in Firefox so the MSE using HTML5 YouTube player doesn't work. This will be why Google would be serving Flash. I don't know if they continue to serve the non-MSE HTML 5 player.
MSE support in Firefox is in progress. Nightly builds can enable it by changing the 'media.mediasource.enabled' about:config setting.
Don't do this though because it will definitely degrade your YouTube playing. Due to an incomplete feature it waits for the entire video to download before playing. There's a patch for this that gets playback working but there are still issues with the adaptive streaming itself (because the implementation is incomplete).
Follow bug 881512 [2] if you want to track support in Firefox for the "Get YouTube working with MSE" issue.
I wrote a bit about this [3] a while back and will do an updated post, if someone else doesn't first, once YouTube support is stable.
[1] http://www.w3.org/TR/media-source [2] https://bugzilla.mozilla.org/show_bug.cgi?id=881512 [3] http://bluishcoder.co.nz/2013/08/20/progress-towards-media-s...