Hey Justin,
I had the same issue. So far, I've found a couple of decent options...unfortunately, neither of them involve Firefox due to its lack of a Flash version past 11.2.xxx. To be honest though, I find Chromium a better browser for gameplay.
Anyway, your two options to get playing again:
1. Install Google Chrome...even the Linux versions come with the latest Flash. A drawback is that the software is coming from Google, not Ubuntu, so it's all third-party and hasn't been vetted. Walkthrough for Chrome install.
2. Install Pepper Flash and you can use Chromium instead. Pepper will be a current version and should work for WGT. You might have to install Chromium since it doesn't come pre-loaded, but it should be in the software centre, so it's an easy "one-click" procedure. Walkthrough for Pepper Flash.
I currently have Chrome installed and working...but I'm going to install Pepper as well so I'll update you on how that plays out. (update - it works perfectly - and really simple to do) If I was picking only one option, it would probably be #2, simply because of the third-party thing. Less potential for messing up the system that way.
Anyway, if any of this gets you back up and running, just drop me off a two-four and we'll call 'er square. ;-)
Jerm