Firefox Flash HDMI No Sound
The solution I've found is to use the HTML5 Video Player.

Flash can be blocked or turned off in "manage plug-in use" - the grey looking lego-type piece with a blue dot at its top right - next to the url:



which, if flash is on, will bring up something like this:



at which point you can block it.

Upon restarting Firefox it will stop trying to use Flash automatically and default to the HTML5 Video Player. The HTML5 Video Player in Firefox has no problem passing audio through HDMI.

Not all flash based videos - or services - can also use the HTML5 Video Player, but for those that can this is a great solution.