There are lots of different things that cause this. If you do a search you'll find quite a lot of information on this.
Most of the suggestions I found by searching Google and LQ did't help me in my situation. After searching for a couple of weeks, I finally found a suggestion that the setting that gives the KDE sound system exclusive control of the sound hardware could be an issue. Mine was set to give exlusive control for 60 seconds, so after I launched Firefox, I just waited over 60 seconds and then went to the Flash content, and to my surprise and delight, it worked fine. I ended up setting my sound system in KDE so that it only had control of the sound hardware for 5 seconds, and as long as I wait at least 5 seconds, I never have a problem with Flash in Firefox anymore.
Like I said, there are a number of other things that can cause this, so your fix may not be the same as mine (especially if you aren't using KDE), but there are a lot of different causes and fixes for this, and lots of info out there.