The offer is valid on bookings made up to January 31st.
If you already have a British Airways American Express then you won’t be any better off using an Amex Platinum or Amex Gold to book British Airways travel. I would also be wary of booking chain hotels via an agent in case you lose your status benefits.
However, this is a very attractive offer for booking, say, non-BA flights. 3 Membership Rewards points per £1 soon mounts up on expensive tickets.