Note that a 32 bit Firefox version will require 32 bit versions of plugins, so make sure that you have the correct version.
Firefox also finds the Flash plugin for me as installed by the Flash installer rpm file
/usr/lib/flash-plugin/libflashplayer.so
As an alternative you can install the Flash plugin (place a symlink) in your home directory /home//.mozilla/plugins/libflashplayer.so
You can try to delete the pluginreg.dat file in the Firefox Profile Folder and maybe addons.sqlite as well to reset the plugin registry databases.
See Re-initializing the plugins database:
https://support.mozilla.org/kb/troubleshoot-issues-with-plugins-fix-problems
OR just see this..
Cross Browser Flash Detection in Javascript