You just need to download and install someAPK files.
Information is also provided on how to root an older Kindle to install Google Play.
Then:
Installing apps outside the Amazon store can expose your gadget to viruses and malware.

Consider downloading a security app such as Malwarebytes Anti-Malware before you begin.
On your Fire tablet, go toSettings>Security & Privacy.
TapApps from Unknown Sourcesto enable it.

If a security warning pops up, tapOKto start the download.
After you have the four necessary files, shut the web client and open theDocsapp on the home screen.
Go toLocal Storage>Downloads.

Tap theGoogle Playapp icon on your home screen to fire up the Google Play store.
You need a Windows PC and a USB cable like the one included with your tablet to do this.
Rooting your Fire tablet voids the warranty.

Carefully consider thepros and cons of rooting your mobile gear.
On your Kindle Fire, go toSettings>gear Options.
Tap theSerial Numberfield repeatedly untilDeveloper Optionsappears directly below it.

TapEnable ADB.In the pop-up screen, selectEnableto activate Android Debug Bridge (ADB).
You may get a security warning; ignore it to proceed.
Connect your Kindle Fire to your setup.
Your PC should detect your machine and download the drivers it needs.
TapOKto Allow USB debugging.
Type2andpressEnterto have the tool plant the Google Play Store on your Kindle Fire.
This process may take several minutes.
You’ll see a message in the window when it’s done.
Reboot your tablet by turning it off and on.
If successful, shortcuts to the Play Store and Google controls should be on your home screen.
Todelete a book, go toYour Libraryon the Kindle Home screen.
Press and hold the book you want to remove and selectRemove From rig.
Totake a screenshot, press and hold thePowerandVolume Downbuttons at the same time for a second.
The screenshot will be automatically saved to your devices internal storage.