Nevermind!! I finally figured it out. I'm not sure what combination of things worked, but for others having trouble:

1. I have never booked with BA before. I needed to open an account, upgrade to their free Executive Club, and confirm my email address. I also loaded my BA Chase card into my account. Until I did all of these three things, I wasn't able to redeem the promo code.
2. Then I went through the normal booking stages: login to AARP and search for BA page, navigate to BA site, the BA site will show that you are getting a discount for AARP, find your tickets, get to the payment page and find where to put the promo code CHASEBA10 (you must be logged in to BA to do this, but you can do it at that step if you need to). The discount will show up on that page, the one that confirms the price.

Then you can decide if you want to pay to select seats, and then you pay.