The step by step guide I think you have worked out:
- install the VeriFLY app, complete the registration information and get your photo to display within the App. So you need a Smartphone for this.
- Connect in your PNR via the App, 7 days to travel, upload vaccination certificates / make attestations as required
- Between 2 to 3 days to travel, use the direct Salesforce link, not the MMB one. Make sure you can upload files such as vaccination certificates if needed and proceed carefully since it's one shot only. Make sure the flight you enter is the flight relevant for the check, e.g. LHR-JFK, not NCL-LHR.
https://digitalboarding.force.com/BA...ionEmbarque_BA
- After you have done this you may get emails and on-screen messages inviting you to submit paperwork even though you have already done this. Unfortunately since the processing is done on other systems (VeriFLY/Salesforce) BA doesn't have full sight of the landscape. These messages can be ignored.
- Or don't bother, do it at check-in instead, where it normally won't take long.
In theory one or the other will work, and if you have VeriFLY then you don't need Salesforce, or vice versa, but I do both as above, and personally I haven't had any problems. As mentioned elsewhere the MMB link will work on direct flights, e.g. LHR-JFK but may be unreliable if your booking is NCL-LHR-JFK.
But if you really don't want to do any of this, which takes me a few seconds, then just do it all at check-in, where it scarcely takes any longer. Just do what you are happiest doing. Note that if flying to the USA there is no avoiding a passport scan, which is a longstanding requirement, though it can be done by the self service machines in LHR, including in Flight Connections, or indeed at the gate.