Many years ago, there was a disagreement between Mozilla and Amazon about how Amazon modified apps in its app store without their publishers' permission. There is an old article on sideloading Firefox for Android on the Kindle, but it doesn't seem to be updated any more, so I don't know whether it's still relevant. If you want to take a look: Installing Firefox for Android on an Amazon Kindle Fire.

Mozilla wanted to put the Android Firefox on the Amazon appstore as Mozilla did have Android Firefox 9.0 up there briefly (in end of Dec 2011?). However it was found that Amazon modified and resigned the apk which caused update problems so Mozilla pulled it shortly after. Mozilla has contacted Amazon many times about modifying this policy, so far Amazon has been unwilling with no progress on this since.

You may be able to side load the Firefox .apk file to it as mentioned. However not sure if you will get updates this way if the install even works. https://www.mozilla.org/firefox/all/#product-android-release