The move sees the video streaming service take on Amazon's Lovefilm, which comes pre-installed on the Kindle Fire and Kindle Fire HD, on its home turf.
Netflix was previously released for Android devices' dedicated app format, and the Kindle Fire edition is a rebranded edition of its Google Play counterpart.
"We are very excited to announce that the Netflix app is available in the Amazon App Store in the UK," said Netflix product manager Roma De.
"Many of you have asked us if Netflix on the Kindle has all the Netflix titles. Yes it does! Everything that is available on Netflix UK is also available via the Netflix app in the Amazon UK App Store."
Earlier this week, rumours emerged linking Microsoft with an acquisition of Netflix to take on the likes of Amazon, Google and Apple in the video streaming sector.
Netflix recently announced that it has reached more than 30 million members around the world, including 5m outside of the US.