After long back and -give I have now decided for an ingenious solution for me. Prerequisite is that you have an iPhone, Mac or iPad.
My solution looks like this:
I bought the Apple TV box from Amazon and connected to the flat. Since I am not interested in the expensive Apple TV media offer so, I now use the so-called mirroring function of the Apple TV box with my Iphone5s. With the iPhone 5s I choose me over the AMAZON LOVEFILM APP Amazon and run on the iphone the video. Via Apple Airdrop (function of the iPhone) is (with the currently playing video) mirrored the display of Iphone5s on my 55Zoll Flat full size. Thus, I use the brilliant Apple technology at fair priced in Amazon Prime video offering.
The Apple TV box is very easy to configure and does 100% what it should.
I am absolutely happy with it.