I have been a audible.com gold member for the past 3 years. I usually use my Nexus 5 or Nexus 7 to listen to audio books. But recently I was forced to use my laptop to listen and it is running Ubuntu 14.04 64bit OS.
So this is what did I do to get it working. I followed this guide to install pipelight a Silverlight alternative for the Firefox browser and went online to audible.com.
Access My Library
and press Play
And it starts up and I am listening on their Audible Cloud Player.