Seems that flash "just works" with the default install of the Chrome browser. At least that's what the flash test page says and Chrome itself tells me that it comes with flash already installed.
Not a very helpful post, but since I installed Chrome browser just to see what happens, thought I'd post my results.
There was a time when it was usually
necessary to manually link libflashplayer.so to the proper location. Maybe this is what's needed in your case? The Fedora Project Wiki
shows how to do this for Chrome.