The FlightInfoEx api can return the unique faFlightID for an instance of a flight if given the ident and the departure time (actual or scheduled). FlightInfoEx can also return multiple entries if the time is not specified or use a faFlightID as an ident to constantly return the same flight.
FlightInfoEx get all instances of CPA543 from newest (normally 2-3 days future) to about two weeks old:
https://flightxml.flightaware.com/json/FlightXML2/FlightInfoEx?ident=CPA543
FlightInfoEx get CPA543 from 01-Feb-2018 based on filed departure:
https://flightxml.flightaware.com/json/FlightXML2/FlightInfoEx?ident=CPA543@1517449500
FlightInfoEx get CPA543 from 01-Feb-2018 based on actual departure:
https://flightxml.flightaware.com/json/FlightXML2/FlightInfoEx?ident=CPA543@1517451293
FlightInfoEx get CPA543 from 01-Feb-2018 based on faFlightID
https://flightxml.flightaware.com/json/FlightXML2/FlightInfoEx?ident=CPA543-1517276700-schedule-0001:2
Multi-stop flights will be broken down to unique faFlightID values per segment. Since epoch time is used and multi-stop flight are tracked per segment there are no flights that can be enroute for more than 24 hours.