I currently do 2FA with with email on a web app, so no phone access required. So anywhere I could get access to BA.com I would also be able to get to my second ID if they allowed email verification.
But from the email we received it seems like they may not allow this option for their version of 2FA.
There are other alternatives to phones that I use for other more secure applications.
One is to have a linked RSA generator where you get a dongle or device and look up a code on there and plug it in. But I suspect they won't want to do that as it costs money.
The other is to have a phone app that essentially does the same thing. But I have not used one of those. Theoretically there is no need for such an app to require a phone signal at the time of use, but it would need internet connectivity when first set up. I don't do apple, so I don't know if that is how Apple Key works.