Amazon comes with its own exclusive app store pre-installed on all its devices, including Fire tablets. However, the app selection here is somewhat limited. Since Fire OS is based on a customized version of Android, you can download the necessary files for the Google Play Store and install it on your device. All you need is an Amazon Fire tablet, a Google account, and four required APK files.
Steps
Check Settings

Open the Settings app on your Fire Tablet. Swipe down the notification bar and tap the gear icon.

Click on "Device Options". This option is located near the bottom of the page.

Ensure your device is updated. Tap on "System Updates" and make sure your device has the latest version installed.
- If your device hasn't been updated, you should do so now.

Find "Device Model". This section displays your device's model and version. Keep this information handy, as you'll need it to download the appropriate files based on your Fire OS version.

Go back to the main Settings menu. Tap the back arrow at the top-left corner of the screen to return to the main Settings menu.

Click on the "Privacy and Security" tab. This option is located in the middle of the page.

Enable "Apps from Unknown Sources". Scroll down to the "Advanced" section. Tap the slider next to "Apps from Unknown Sources" to turn it on.
- You will receive a warning about installing apps from unknown sources. Tap OK.
Download the File

Determine the version of the file you need. The file has two versions: 64-bit and 32-bit. The version you need to download depends on your Fire OS version.
- If you're using Fire OS 6 or later, download the 64-bit file.
- If you're using Fire OS 5 or earlier, download the 32-bit file.

Download the Google Account Manager file. Select the version suitable for your tablet and click the red DOWNLOAD APK button.
- Download the 64-bit version at https://www.apkmirror.com/apk/google-inc/google-account-manager/google-account-manager-7-1-2-release/google-account-manager-7-1-2-android-apk-download/.
- Download the 32-bit version at https://www.apkmirror.com/apk/google-inc/google-account-manager/google-account-manager-5-1-1743759-release/google-account-manager-5-1-1743759-android-apk-download/
- Don't install the file just yet. Leave the file in the notification area for now.

Download the Google Services Framework file. This file works for all versions of Fire OS.
- Open https://www.apkmirror.com/apk/google-inc/google-services-framework/google-services-framework-5-1-1743759-release/google-services-framework-5-1-1743759-android-apk-download/ in your web browser.
- Click the red DOWNLOAD APK button to download the file. Don't install the file yet.

Download the Google Play Services file. Choose the version suitable for your tablet, then click the red DOWNLOAD APK button. Don't install the file yet.

Download the Google Play Store file. This file works for all versions of Fire OS. Don't install the file yet.
- Visit this link.
- Scroll down to find the latest file.
- Click the downward arrow next to the date to download the file.
Install the file

Open the notification area to locate the downloaded file. Do not open any apps after installing—just click 'Done' and proceed with downloading the next file.
- If you encounter an error, you may have downloaded the wrong file for your device.

Install Google Account Manager first.
- Find the file in the notification area. (If it's the first file you've downloaded, you'll select the last file in the list.)
- Tap on the file.
- Click Next.
- Click Install to proceed.

Install the Google Services Framework. This file is the second one from the bottom in your notification area. Just tap on the file, click 'Next' in the window that appears, and then tap 'Install'.
- Find the file in the notification section. (If it’s the second file you downloaded, choose the third one from the list.)
- Tap the file.
- Click Next.
- Click Install to finish.

Install Google Play Services. The download might take some time; do not cancel the download or turn off your device.
- Locate the file in the notification area. (If this is the third file you downloaded, choose the second one from the list.)
- Tap on the file.
- Click Next.
- Click Install to confirm.

Install the final Google Play Store file. The download may take a while; do not interrupt the process or power off your device.
- Find the file in the notification section. (If this is the last file you downloaded, select the first file in the list.)
- Tap on the file.
- Click Next.
- Click Install to proceed.

Restart your device. Once all files have been installed, reboot your device to complete the installation.
Sign in to Google Play Store

Launch the 'Play Store' you just installed from the app list.

Sign in to your Google account.
- If you'd like to create a new account, tap on 'Create account' at the bottom-left corner.

Fill in all the required login details and follow the on-screen instructions.

Use the Google Play Store as needed. After signing in, you'll be taken to the Google Play Store where you can download any apps you wish.