Just wait for a bit for a more seasoned FTer to respond. I know that you can't get platinum bonus if you already have another Amex-issued card, but yours is the other way round.
Note the terms say this:
1. 18,000 bonus Avios will be awarded onto your account once you have been approved and a minimum of £3,000 on goods and services has been spent and charged to the account within three months of account opening. If you are a British Airways American Express Credit Card or British Airways American Express Premium Cardholder, you will not be eligible for this offer and this is not an offer to upgrade. Please note that it can take up to one month for bonus Avios to be awarded to your account. Offer expires at midnight on 12 September 2012.
So this only excludes the BA cards, not the Platinum card.
This is the thread at the BA forum but it is massive:
http://www.flyertalk.com/forum/briti...er-thread.html