I have written a pretty extensive article before, on “How to install Kodi on Amazon Fire TV“. It’s still an article worth reading, but a better “trick” has become available.
In the previous article, we used an application called IkonoTV as a “front” for Kodi/XBMC. This method works well, but has it’s limitations. The new method is easier to install, doesn’t need an application like IkonoTV and … the home button on the remote brings you to a screen that just works easier.
Another important feature is that this new method is supposed to work with the newer Amazon Fire TV models – unfortunately, I do not own the newer model, so I could not test and confirm that.