I don't know why they don't play on your Mac, but my guess would be you either don't have the plug-in or that the file association is wrong. As for downloading flash, I don't have that problem in Winders.
When you're creating Flash files..you can pick which systems that it'll play on. I'm guessing that either your system ain't got the right plug-in, or most of the programmers have forgotten all about MacOS, when converting their files.