I have no experience of this in the order that the OP plans to fly - misconnecting to an AA flight because of a delayed BA flight.

I do, however, have experience going the other way around - misconnecting to a BA flight because of a delayed AA flight - and it wasn't a good one.

Our AA DEN-ORD-LHR flights were seriously delayed because of weather. AA rebooked us on our connecting LHR-EDI flights (which were on separate tickets) and issued us with BPs and checked our bags all the way through to EDI.

When we came to board the EDI flight at LHR we were denied boarding by the BA GAs. We were given the choice of buying new tickets or having our bags unloaded. We tried to tough it out, reckoning that common sense would prevail and that they wouldn't delay the flight just to get our bags off. Wrong! Bags came off and we had to buy new tickets.

BA offered us a 'special unpublished fare' that they have to 'help' people in this situation. Asked at the BD counter - they offered tickets at significantly less than the BA special.