Amazon video now works great under Linux. Once Amazon had rolled out an HMTL5 player it was no longer necessary to spend time on workarounds because there was no Linux version of Silverlight. Of course Google Chrome is a necessity, other browsers can't be used.
There seems to be a compatibility issue with running the Amazon player under Gnome 3, a distracting white border appears down the right hand side of the screen and along the bottom. Using a window manager (like the excellent Openbox) solves this.
Another quirk is that the mouse pointer doesn't disappear automatically when using a window manager. Right clicking solves this although you have to wait for the player overlay ("Options", volume control etc.) to fade out.
