Qtaqua, welcome to FlyerTalk.

This really isn't the right forum for your question, which is probably why you haven't received any responses.

But since we are here, I will try and provide you with a bit of information that may help you with your quest.

There really is no efficient way to transfer or combine miles between AA and BA programs, or vv. I suspect you may be able to transfer your AMEX points to one of the airline programs, but I know very little about AMEX ( I assume you are a USA based cardholder ) so someone else will have to provide that info, or you can probably find it on the AMEX website.

There really shouldn't be any need to transfer or combine miles between accounts if you are looking for economy class tickets. You will need 50K BA miles for each round trip ticket, or 70K AA miles for the same ticket. So you already have enough miles in either account to make it happen. You will end up flying on either CX or JL regardless of which programs miles you use. Availability of reward seats should be more or less the same using either BA miles or AA miles, so naturally my choice would be to use BA.

I think the most important advice that I could offer is BOOK NOW! If you are determined to fly over the Christmas holidays award seats will be very hard to find.