Amazon video used to use two forms of video streaming. Silverlight and Adobe Flash. Amazon has totally dropped Flash as a choice after switching mostly to HTML5 which can be used on IE 11, Edge browser, Chrome browser, and Opera Browser. This can be done just by installing one of those browsers.
Of course IE 11 and Edge are Windows browsers only. I cannot tell you why Safari supports HTML5 on Netflix as of Safari in Yosemite or higher. But I can tell you that in El Capitan Silverlight has some real issues in full screen mode with Safari. Chrome has dropped supporting Silverlight and uses only HTML5 streaming for Amazon and Netflix. If you are having issues with Silverlight in Safari viewing Amazon or Netflix. I suggest you install Chrome or Opera. Firefox also does not stream HTML5 for Amazon it also uses Silverlight. I know Firefox reluctantly added function for Netflix because the DRM Netflix uses is not open source. I am not sure why Safari is still stuck with a poorly performing option of Silverlight and not HTML5? But apparently for Amazon its about numbers. More people use Chrome so that was one of the first browsers to support Amazon's HTML5 streaming. One last note, Microsoft is basically advising everyone using Silverlight in content distribution or viewing to move to HTML5. So its of no surprise that Silverlight is on the long list for fixes in Safari. My advice to anyone viewing Amazon video content to switch to another browser that can do html5.
