AA would have gotten you to IAD, just likely not in time to meet a flight on a different carrier and different PNR. I think the most you're owed here is a refund of your BA Avios points since your original flight was cancelled. Do you know why the original flight was cancelled? I'm not sure that matters much here, however, since it cancelled at your origin and you chose to not fly on AA at all as a result. AA would typically refund the flight if this had been booked through them.
I suspect the plane ran low on fuel after having to sit on the tarmac due to the ATC issue. I don't think AA owes you any compensation for the ATC failures and downstream impacts of that. And, AA had no obligation to deliver your bags to Cape Town, only back to you at DFW or, had you flown AA, to you at IAD.
AA may give you some points (if you're an AAdvantage member) but that's likely it.
As others have said, this illustrates the risks of separate bookings such as this. It may save some money but ultimately may not be worth the risk and stress.