Getting Flash updates to work reliably in Firefox in Ubuntu Linux is a common problem, even a simple security update can break it - and did for me.
The fix was to make sure ALL traces of Flash have gone (swfdec-mozilla was the one causing a problem for me):
sudo apt-get purge adobe-flashplugin flashplugin-nonfree gnash gnash-common libflashsupport mozilla-plugin-gnash nspluginwrapper swfdec-mozilla
Then install the latest, with:
sudo apt-get install flashplugin-nonfree
I don't know if it's required or helps, but I kept Firefox closed while doing this. No reboot was needed.