I was having the same problem with Window 7 (64bit), Firefox 20.0.1 (and in prior versions) and with AFP Ver 11.7.700.169 (and previous versions).
With Firefox, I have several add-ons. So I restarted Firefox in Safe Mode and was still received the same error message.
I was able to stream Amazon Instant Videos (with all Firefox add-ons enabled) after visting the Flash Player Settings Manager website - The Settings Manager is a special control panel that runs on your local computer but is displayed within and accessed from the Adobe website. I made the following changes (I have provide the according links).
1. Protected Content Playback panel - I selected the "Reset License Files" button. Link - http://www.macromedia.com/support/documentation/en/flashplayer/help/se ttings_manager08.html
2. Website Privacy Setting panel - I selected "Always Allow" for both "ecx.images-amazon.com" and "amazon.com". Link - http://www.macromedia.com/support/documentation/en/flashplayer/help/se ttings_manager06.html
3. Website Storage Settings panel - I increased the storage from the default 100KB to 1MB for both "ecx.images-amazon.com" and "amazon.com". Link - http://www.macromedia.com/support/documentation/en/flashplayer/help/se ttings_manager07.html
After the above changes I was able to stream Amazon Instant Videos. It is possible that only 1 or 2 of thes above changes were necessary, as I haven't tried to recreate the original problem.