It’s hard to believe, but the screenshots in this post are not images of the Fire TV interface. They are screenshots of Kodi. The incredibly skilled Kodi skinner Kevin (aka Hitcher) has released a skin for Kodi that makes it look exactly like Amazon’s Fire TV interface. He has been working on the skin for months and just released the first alpha version. It looks absolutely amazing and perfectly replicates the Fire TV interface, down to the tiny nuances. You can download the skin from here, and while you’re there, hit the donate button on that page to support Hitcher’s efforts and show your appreciation.
Note that this skin works best with the new “Isengard” beta version of Kodi. See the thread linked above for more details. Thanks kingofenglandrew for pointing that out in the comments.