I have landed as late as 3:30am. AA actual has a scheduled flight at times that departs DFW around midnight and lands at DCA at around 3:45am.
Here is AA schedule for July 16, 2017
AA 2293 DFW-DCA 8:15pm - 12:13 am (daily except Sat)
AA 2690 DFW-DCA 11:50pm - 3:49am (Sun only)