As noted by RichieMc to UuA an AA operated flight you must be on a BA ticket (125-) and you must be booked under the AA prime code. You obviously have the BA ticket part right, the BA prime code will be stopping you in your tracks. As this would be an avios upgrade you should not receive any extra avios or TPs. See Part 03 of this post in the Guide:
https://www.flyertalk.com/forum/32910040-post7.html

As for cash upgrades, you can look at your itinerary in the AA app where AA sometimes offers upgrades in advance of flight. At JFK you might be able to pay cash to AA to upgrade J to F by asking at the lounge. Neither of these methods should earn you extra tier points or avios unless a mistake is made. At JFK you could try to do a fare difference upgrade (pay the difference in the fares between your business class fare and the regular cost of the first class fare) but I seriously doubt that AA will do this as you are on a BA ticket with additional BA segments still to fly.
Paid transcon first upgrades on day of travel
https://www.flyertalk.com/forum/brit...con-j-f-5.html