AA 3865 then AA 3867 at Charlotte
Hilton Head → Charlotte → Key West
Timetable, Charlotte time
13:44AA 3865 from Hilton Head at the gate
12:45AA 3867 to Key West leaves the gate
23 h 01 apart on the timetable, overnight
AA 3867 leaves 23 h 01 after AA 3865 arrives on the timetable: more than half a day, so not a connection we count.