In former times the Flash Player was provided as a tar.gz. An additional project created pre-packaged versions for various distributions. This has changed now, Adobe is providing rpms on their main download page.
In former times (read: Macromedia times) the Flash Player for Linux was provided as a tar.gz archive. Other packages were available via a community project driven by Warren Togami. This project was tolerated, but not officially supported.
This now have changed: today I realized that the official Adobe download page for the Linux version features a rpm version as well as the tar.gz version. Looks to me like Adobe really tries to make Linux a first class citizen. And before you now ask for deb packages (which would be cool anyway) please keep in mind that that rpm is the LSB format – whether you like it or not However I’m not sure if this package is LSB compliant.
Fortunately there is still Warren’s community page – this has all the necessary packages and also provides repositories. Providing rpms is very good, but nothing beats a native repository.