Hi my name is ***** ***** I will be the expert working with you today to help and resolve the problem you have posted.I am sorry to hear that you are having such trouble. I will try my best to help you out and resolve the problem as quick as possible.
you cannot get a gmail address with .com.au as its not a general google australia service it provdide for free email as gmail service, however if you own a business online and you have an email ending with .com.au or .au then you can use it with gmail and that service is a paid service from google.
What email does it say does not exists
let me know the gmail address
do you have access to this***@******.*** email without a problem, i mean you can send and receive emails?
so the problem is that the flight booking account is not recognizing your gmail account is that correct?