Couple of points.

Why are you using your father's card rather than your father making the booking? Some card issuers may be concerned about this.

My second point is if the cards being used are South African as it is treated as a high fraud risk country. If you try to put through one or more third party transactions, you may well run up against either BA or bank any fraud measures. In such circumstances I would have thought it better if the card holder were the one who dealt with the bank and having to say to a South African bank that the transaction is being performed by a third party in the UK is not going to make matters any easier.

When I have booked flights for others, I have always put the transaction through myself, putting in their BAEC numbers so that they can then manage the bookings. That certainly works.