If you need to know whether a web browser supports Macromedia's Flash format, Colin Moock provides a script at http://moock.org/webdesign/flash/detection/moockfpi/, which you can use on your web server to determine whether a visitor to your site has Flash support in his or her browser and whether the version of Flash supported is the currently available version. As he notes on his website, Flash detection methods can't provide 100% certainty. He estimates that you may be able to reach a certainty of 90% to 97%.
I've included his code on a webpage at the link below that you can use to test whether a browser on a particular system has support for Flash.