Current workaround is to set up Two Factor on your Amazon account, then logout & attempt to sign into Amazon your phone's browser to trigger a one-time two factor code to be sent to you, then set up your Deliveries amazon sync with the code added to the end of your password (no spaces). It's come up in other threads. Just used this on my new phone today, still works.
Edit: I see you've seen this fix, but I would add that you really want to make sure you're using a browser to generate a new code and not use the code until you hop over to Deliveries to make absolutely sure that one-time code is expecting a generic login attempt and not from the Amazon app or other specific source. Also, don't reuse a code that has failed - the login requests really are hitting Amazon, so if the code has been used, the code is now invalid and you'll need a new one.