I've dealt with this before. There appears to be a difference between the Flash plugin that is installed within the browser, and the one that works better.
(This also seems to resolve the issue of videos spontaneously stopping and restarting themselves in Firefox and Chrome.)
I recommend using Synaptic to check this, but the instructions below are for the terminal...as you probably don't need me telling you what to click in Synaptic, ha ha.
sudo apt-get remove flashplugin-installer
That removes the rather glitchy version that gets parked in the browser when you install from the Adobe Flash website.
sudo apt-get install adobe-flashplugin
(For the record, that one is version 11. Version 13 is not yet available for Firefox, as user7134 correctly stated.)
That installs the plugin, which works a LOT better. That's the only one I have installed on my Ubuntu 14.14 system, and Firefox and Chrome are quite happy.