You don't need to do much, if on Android you will get a notification which leads to a BA screen - click on the three dots top right, and "Use WiFi without login" or "as is" or similar wording. Then it connects, and you then don't need to do shop.ba.com (though it's confirmation that all is well) - the app should just work. Note that aspects of the app use external bots, notably if you try to pay for something and the bank authorisations kick in. But the guts of MMB should work. I would have another go when on the next booking - you may not be wanting to use the app when flying, generally, but this is all about knowing how to get connected when it's really useful to do it.