Restore backup.ab file on firestick?
If the device is rooted you can manually restore the backup. 


On a PC extract the backup file using Android Backup extractor. 
This will convert the backup to a TAR archive.
(optional) extract the APK files (if the backup contains not only app data) and install them via adb.
Upload the TAR archive to your device via adb push and untar it.
Copy the files you want to recover into the right directories using adb shell and root permissions.