[stumped]

There are 2 solutions here.
1. Is install Google play on fire,, buy from Google, but maybe the op has an old Kindle fire so that does not work.
2. Buy moon from Amazon store, they happily sell it to any device or virtual device that is not a fire, then backup and sideload. That works if the purchasing device and the target device use same Amazon account. The Amazon version is never quite as up tomcats as the Google version but this is a stable app, so no big deal.
And for the record, others say that moon pro from Google play does not do a regular licence check so once you have bought it , it can be copied and re used? I am surprised the author does not see the need to block that..
Amazon store checks licences daily..

I use method 1 now, but I used to use method 2, before I learnt how to install Google on fire
We have several fire devices but I cannot add Google to the oldest one that is running os 4. Wasted hours trying. For os 5 it is easy, but there's is no guarantee that Amazon will not block it at some point. And some folks have problems with 2018 models. There was a long recent thread about adding Google to a 2018 fire hd8, where the OP got into a Terrible mess