I found this thread http://fedoraforum.org/forum/showthread.php?t=192887 on the topic. The piece that helped me out was
su
yum -y install gtk2
rpm -ivh http://linuxdownload.adobe.com/adobe-release/adobe-release-i386-1.0-1.noarch.rpm
yum install flash-plugin.i386 nspluginwrapper.x86_64 nspluginwrapper.i386
yum install libflashsupport.{i386,x86_64}
mozilla-plugin-config -i -g -v
I closed and restarted Firefox. It worked like a champ.
