Apple Music is steadily expanding its territory on third party devices, Apple introduced Amazon Echo support in the USA back in December and is now rolling it out to the Fire TV as well.
Apple says support will be coming to the U.K. in the coming weeks. To start using Apple Music on Fire TV, enable the Apple Music skill in the Alexa app, you can then ask Alexa to play your favourite song, artist etc. ensuring you say Apple Music in the phrase for Alexa to understand. If you already activated Apple Music for Amazon Echo, it should be available on Amazon Fire TV automatically.
Original source 9to5mac