Firefox hasn't used Flash to play videos for a good while, unless an HTML5 copy isn't available on a web site. As I recall, the problem is a volume level one.

But whatever is causing that problem, its worth noting that Firefox won't automatically play videos in more recent versions. There is a play button Firefox places on the screen which you activate. I don't use Firefox much, but I've seen more than one play button at times and the one at or near the top of the screen does nothing. You have to find the one farther down.

That's actually a good feature for blind people, preventing sites from playing unwanted audio when a screen-reader is being used.

Gene