The Amazon Fire swc app will not allow you to connect to Google Play. You need to download swc from Google Play. Unfortunately, when you do that, swc does not load. Therefore, you can't even get the base stored/saved on Google Play. I sync'd it to FB, but the FB version stored from the Amazon tablet, cannot be pulled into the Android tablet. I tried and it does not even come up as an option to sync.
I think you only need the Facebook account to move it over to the new device. A family member (with no SWC already synched to it) can, if they loan you access to it for a day, help. Once you pull it down to the new device, Game Center on iOS or the Play Store back up will suffice. You don’t need FB after the move. But even you did, Uncle or Aunt somebody probably wouldn’t care if some SWC game were pegged to it. They are unlikely to download Gameroom to access it, cook Banthas/probe droids, send wall messages to them or otherwise mess with the kid’s base. Though they could
ALL AMAZON GAME DEVICE PLAYERS - Remember to Sync your game to Facebook and grab a Screenshot of your Player ID found in Settings > About.
As a final resort, Disney may be able to transfer your Old SWC Account Info to a New SWC Account Info.
See the following Official Help (scroll down to bottom) found here.