If it were as simple as that, Linn would have achieved it by now. I’ve been asking them for over three years since Amazon Music HD came out and Amazon don’t seem to want to interact with Linn or are putting barriers in the way of them being able to support it - for example, Linn have said it would only be their newer models (like Selekt, MDSM/4 and I guess now Organik) that could support it due to some hardware requirement specified by Amazon. I have no idea what that might be. I understand Naim have similar difficulties. Maybe Linn and Naim aren’t sufficiently well known or have a large enough market share to warrant Amazon’s time in supporting their development efforts.
Similarly, if all it took was registering as a developer, we would have seen Amazon Music implemented on LMS and similar user driven platforms before now. I think there was a rumour that Volumio might be looking at supporting Amazon Music but I don’t know how far that’s got, if indeed anywhere.