Check your Fire tablet model and Fire OS version
Back up important data
Open Settings
Go to Security & Privacy
Enable Apps from Unknown Sources for Silk Browser or Files app
Download the four required APK files from a trusted source
Google Account Manager
Google Services Framework
Google Play Services
Google Play Store
Install the APKs in this order
Google Account Manager
Google Services Framework
Google Play Services
Google Play Store
Restart the tablet
Open Google Play Store
Sign in with your Google account
Update Google Play Services if prompted
If Play Store does not open, clear cache and data for Google Play Store and Google Play Services
If needed, uninstall the APKs and reinstall them in the correct order
Keep Fire OS updated for compatibility