I haven't used the Amazon streaming service, but I found this on the wiki. Not sure if it will help but I cut and pasted.
"By default, AIV uses Flash Video in all web browsers with the Adobe Flash plugin installed. This feature was launched in public beta July 17, 2008 and was released September 4, 2008. Using Flash should make AIV relatively portable (compared to, e.g., Netflix Watch Instantly). AIV has been reported to run well on Linux distributions.
Customers may also download videos to TiVo Series 2 and Series 3 DVRs, except those made for use with DirecTV (DirecTiVo). Sony BRAVIA TVs equipped with an Internet Video Link device, and Panasonic VIERA TVs equipped with Viera Cast can also use Amazon VOD directly through the TV's menu system. As of April 3, 2012 the Sony Playstation 3 officially supports Amazon Instant Video. As of May 19th, 2012 Amazon Instant Video announced it would be available to Xbox 360 users, via Xbox Live. 
The optional Amazon Unbox player lets users download higher-quality copies of videos. The Unbox player is compatible only with the Windows XP family of operating systems, Windows Vista, and Windows 7. Downloaded films include a full-resolution video file and can include a lower-resolution copy for portable devices. The content can be viewed using the Amazon Unbox Video Player, Windows Media Player, a Windows Media Center Extender such as an Xbox 360, a PlaysForSure portable device. Downloaded videos may be burned to a DVD for storage purposes, but the resulting DVD will not play on a DVD player.
It is not compatible with Apple TV."
The last paragraph discusses HD. Looks like you would need to play it in Windows Media player.