This is an optional method to install Google Play store on your Fire Tablet, then using the Google Play Store, Emby.
This should work on Fire OS 5 onward for Amazon Fire tablets with no Root, PC or ADB required.
In order to easily install APKs you will need a file manager. If you don't have one already we can recommend TOTAL COMMANDER from the Amazon Appstore.- https://www.amazon.co.uk/dp/B00H4IHJ8M/
Note: You will need to enable 'Apps from Unknown Sources' found under Settings > Security of the Fire OS.
Now download each of the following APKs from a web browser (SILK) and install them in the order below using TOTAL COMMANDER.
1. Google Account Manager 5.1-1743759
2. Google Services Framework 5.1-1743759
3. Google Play Services 11.5.09 (230-164803921)
4. Google Play Store 8.3.41.U-all  [FP] 170066753
Once these are install, POWER OFF and RESTART your tablet.
You can now open the Google Play Store and log in with your Google account.
You can now search for Emby and install it on your Fire Tablet along with other Google Playstore apps.
Once apps are installed the Google Play Store will auto update these apps in the background.