I heard this happen to a colleague recently so he decided to just close the card entirely and leave Amex. Amex then changed approach to get him to stay, believe offered him some free points, which he duly accepted.

I recently went to downgrade to the Blue and was offered a new spend bonus on the Premium.

To answer the question - once the companion vouchers are in your BA account they are yours BUT the rule is that you need a BA Amex (either blue or black) to spend the requisite surcharges on. I.e you need to use your BA Amex to redeem your voucher, so afraid you can’t cancel BA Amex altogether and still use your voucher.

Back to the OP - I’m sure as you have flights booked it will be fine - though unless I’m mistaken there is some small print somewhere that you may be asked to show the card that you booked with to fly. For those of us who change credit cards often that would be a problem, so it clearly happens very rarely/almost never, but I have read about it on this forum. I am sure a true expert will be along to clarify about that shortly.