Google Play Store is one of the most capable app stores out there. It comes usually pre-installed on Android devices, but it is not available for other devices. Amazon tablets users have to limit themselves to the Amazon Appstore.
However, since the Fire Tablet uses the Fire OS, an Android based OS, you can still install Google Play Store. There are more methods that you can use.
1. Get the Google Play Store from a Windows PC
This option is a bit more complicated. You will need a USB cable and a PC.
Open the Settings app on your Fire Tablet and then select “Device Options” under Device. Scroll down and you should be able to find the “Serial Number” field. Tap it at several times until a “Developer Options” option pop up below it. Tap it.
Scroll down until you find the “Enable ADB” option and then tap it in order to activate it. Just as the name suggests, “Developer Options” was created for developers, so proceed only if you know what you are doing.
Connect your computer to the Fire Tablet. Now download the “Amazon-Fire-5th-Gen-Install-Play-Store.zip” file from the Root Junky website. Unzip the file to a folder. Now double click on “1-Install-Play-Store.bat”
Unlock the tablet and “Allow USB debugging,” then when you reach the first screen type 2 and then press Enter. You will be asked to reboot your tablet, do that. Now you can unplug the tablet and you should be able to find the Play Store and the Google Settings shortcuts on your screen.
2. APK files
For the second option you will need to go to Settings and enable “Apps from Unknown Sources”. Now you will need to download four APKs: Google Account Manager APK, Google Services Framework APK, Google Play Services APK (use this version instead of if you have the 2017 Fire HD 8), Google Play Store APK.
Download them all and then open the Docs app on your Fire tablet and tap “Local storage” Select the Downloads folder and you should find the files, tap on them to install them (in the order they are in the list).
After they are installed you should be done.