It looks like you don't need to scan anything when exiting. So your phone could die once you're in the store and you'd still be able to check out.

I'm guessing the Amazon Go app generates a one-time-use QR code that gets scanned on entry and then security/tracking cameras follow you all over the store. If the cameras see you in front of an item when its RFID sensor detects it was picked up, they make an educated guess that you picked it up. Then they can re-scan all the RFIDs as you exit for extra confirmation.