They were using Silverlight on the web. They had Flash at one time, but I think it's been a while; they've been using Silverlight for a few years. They've been pushing into HTML5 video, though I don't know the current state of that rollout

http://www.geekwire.com/2015/amazon-starts-rolling-out-html5...

Not sure if this is true for all vidoes, but I have watched several shows on Amazon using Chromium, and I don't have Flash installed.