The very first thing I did with my new Amazon Fire HD 10 was to install the Google Play Store.
I love Amazon's bargain tablets, they are a cheap Android device with heavy integration into Amazon. I ignore the shopping and love the Prime Video. Installing Google Play store gives me access to all the stuff Amazon doesn't provide: Gmail, Chrome and thousands of Android apps.
The process is very simple and only requires you download and permit four .apks to install (all files come from APK Mirror):
You will have to permit the files to be installed as Amazon doesn't love Google as a source.First: Google Account Manager 7.1.2 (Android 6.0+) Second: Google Services Framework 9 (Android 9.0+) Third: Google Play services 19.6.29 (100300-278422107) (100300) Fourth: Google Play Store 17.5.18-all  [PR] 280467566 (nodpi) (Android 4.1+)
This is my fourth such Amazon tablet and I have never had an issue with Amazon trying to block this activity.
The new Amazon Fire HD 10 has some decent CPU and memory upgrades. I am trying it out this week and will review soon. Thus far, its the same as the old one but faster and with a slightly better screen.