I migrate from Xbuntu to Crunbhbang Linux a couple days ago. Until today, I have not have a chance to test amazon prime video service yet. I try today, and guess what I can not watch video any more.
I look around for solution, and found this Ask Ubuntu page, which intern point to the Adobe support page that contains the solution. I make a copy over here for my own reference :)
Prerequisites for protected content playback
For Ubuntu 10.04 or later, ensure that the Hardware Abstraction Layer module is first installed using apt-get.
(Watch carefully for “hal” install errors, as a damaged package install can continue to affect video playback.)
sudo apt-get install hal
After the "libhal" (HAL) library install completes, close the browser and clear the Adobe Access directories by executing the following shell commands:
cd ~/.adobe/Flash_Player rm -rf NativeCache AssetCache APSPrivateData2
If the Hardware Abstraction Layer module is missing, Flash Player still functions. However, it cannot play protected content that requires the Adobe Flash Access DRM (Digital Rights Management) module.