I use AutoPlus to install Flash on my fedora installs. (Note: I use 32 bit and it works flawlessly).

Link:
http://www.dnmouse.org/autoten/

Note: Originally called Autoten, then FedoraPlus, now AutoPlus. I have no idea why the constant name change. I've used it since F11 and it always installed my adobe apps, codecs, etc. just fine. Although I would stay away from Adobe Air and Tweetdeck, since there always seems to be problems installing them.

Edit: Just noticed on the menu on the website, the word "Uninstall" whatever app shows. When you install AutoPlus, all the menu options are set to "Install", then, after installing an app, when the menu comes up again, those not installed say "Install" and those that have been installed say "Uninstall". That's a bit confusing, I'll have to mention it to Dangermouse. I guess he took the screenshot on one of his machines that had everything installed and didn't notice.