None of AA's (or TW's) SP's came from Braniff.
N601AA and N602AA were both leased from TWA (who also did all the heavy maintenance on them) between 1987 and 1992.
Originally known as N57202 and N57203 at TW.
Originally leased to operate DFW-NRT until the MD11's arrived, at which point they moved to JFK-LHR in 1991. They were returned to TWA in July 1992, but were almost immediately sold.
N601AA found its way to a couple different operators. Just weeks after a very hard landing incident at STN in 1999, cracks were discovered in the main landing gear while undergoing a check at LUX, and the owner simply abandoned the aircraft. Two years later, the airport authority seized the hull for non-payment of landing/parking fees, and it was scrapped in 2002.
N602AA wound up in a VIP configuration for Dubai Royal Flight, and was later sold and is still in service with Ernest Angley Ministries (a miracle worker based out of Akron/Cleveland who does stadium tours...) under the name "Star Triple Seven"..
The third 74SP-31 ordered by TW was N57201, which is now a VIP transport for the United Arab Emirites.