This is a problem that I've been trying to resolve for a few weeks now and have just resolved it
I'm using Mandrake 9.2.
I found that installing the Flash-Player alone is not all you have to install.
I did the following:
1/ Download the Flash RPM file.
2/ Double click on the Flash RPM icon - this installs the Flash Player.
3/ Click on K (in KDE) or the GNOME footprint button -->Configuration-->Packaging-->Install Software.
4/ After typing in your Administrator password the Software Packages Installation window will appear.
5/ In the Search box type 'Flash' (without the inverted commas), click on the 'Find' box and change to 'in descriptions' and then click search.
6/ After a short while, four or five files will be listed. Tick the boxes of all these files and click on 'Install'.
7/ After a few seconds, the packages will have installed.
8/ Close the Software Installer window and that's it!
When you start up Mozilla, the Flash sites will work.
Hope this info helps somebody out there. I couldn't find any Geek-speak-free info to help me and I just tried this as a shot in the dark and it worked