The last piece of the puzzle for trying to run one of my systems solely on Linux fell into place a couple of weeks ago. I tried the KDE flavor of Linux Mint 12 (Lisa) in a virtual machine and was able to watch a Prime Instant Video.
That was enough for me and I put Linux Mint 12 on my old laptop. Running from a straight boot rather than in a virtual machine added a little complexity, but by Googling, I found that I needed to install the Hardware Abstraction Layer (HAL) package. After I installed that, Prime Instant Video has worked without a hitch.
Prime doesn't have the exact same selection as Netflix. Some things that Netflix has for free (like "Breaking Bad" - at the time of this writing) are only available for purchase at Amazon, but there's still LOTS of free stuff at Amazon that you can watch on your Linux machine.
I know it seems stupid that Netflix won't support Linux, especially when it's on Android phones and Chromebooks, both of which have Linux underpinnings. But since we can't seem to change their minds, at least Amazon is willing to welcome us.