Is there any way to watch Amazon Video on Samsung Gear VR?
There was some speculation around March 2016 about some job offers posted by Amazon, that some commentators interpreted as a hint that they were preparing a VR app for their video service. See this article for example.  

However, more than one year later no official statement by Amazon has been issued, and no app has appeared.  

It seems that the only alternative currently is to use the unofficial application SideloadVR, as suggested for example by this post answer.

However, it seems than currently not all the Gear VR devices are supported, as suggested by the reviews (and developer replies) on the Play Store. In particular support for popular Galaxy S8/S8+ devices is yet to come.