Open Settings on the Fire tablet
Tap Security & Privacy
Turn on Apps from Unknown Sources
Open the Silk browser
Download the four required APK files from a trusted source
Download Google Account Manager APK
Download Google Services Framework APK
Download Google Play Services APK
Download Google Play Store APK
Open the Files app
Install Google Account Manager APK
Install Google Services Framework APK
Install Google Play Services APK
Install Google Play Store APK
Restart the Fire tablet
Open Google Play Store
Sign in with a Google account
Update Google Play Services and Google Play Store if prompted