How are flight schedules displayed without ambiguity on DST change days?
It's only really ambiguous once a year, when moving from summer time to winter time and the hour is 'repeated' - in this case, departures and arrivals are scheduled in the 'first' instance of the hour: eg if the flight is scheduled 01:30, it will depart 1.5 hours after midnight. The clock will then go back eg at 2am, and the airport will be relatively for one hour with no departures (although, of course, arrivals may still come in)

On the other shift, the hour is 'lost' so the departure takes place later. In practice, no planes are scheduled to arrive or depart in this missing hour, and since almost all nations make the change in the middle if the night when airspace is very quiet and most airports have no departures at all there is virtually no knock-on effect. Arrivals arrive when they arrive, departures are simply scheduled for a 'real' hour, if there are even departures at all at that time of day anyway.

Note that this is only for passenger scheduling - in air traffic control etc all times are Zulu (UTC) which has no ambiguity.

TL;DR: Fall/Autumn, aircraft depart in the "first" instance of the hour. Spring: scheduling works as usual, but with no flights scheduled in the "missing" hour (eg 2-3am)