Because of this, it took me about two hours of cursing to figure out how to get any Flash webcam widget to work on Linux. The reasons for this were both that Flash is 1) incredibly unstable on my version of Linux, and crashes every 20 seconds (when there are flash widgets running at the same time on different pages), and 2) it asks for permission to use the webcam, but there is no way you can click on the 'allow' button. The only button that works is tab. Spacebar, enter, etc. don't work, so you can't allow access. Maybe you're experiencing the same thing. Then I can save you some time and cursing:
The answer is to go to the Macromedia Flash website, where they have a settings page with a Flash widget that actually changes your local Flash settings. You can find it here:
Now, for making nimbb.com work, for instance, add nimbb.com (or player.nimbb.com, or static.nimb.com, or whatever domain is asking for permission) to the Global Security Settings panel (shown above), AND add it to the Website Privacy Settings panel (shown below). For the latter, you have to have visited the site before, in order to have it as an option. So if you've just visited nimbb.com, for instance, it would be shown right at or near the top:
Now, reload the original page you were trying to view, and the webcam and microphone should be working.