How to create a trigger that will insert values into another table twice?
So the following trigger works perfectly to prevent double bookings for the case stated in the question:

CREATE OR REPLACE TRIGGER Check_Double_Booking
BEFORE INSERT OR UPDATE OF Aircraft_ID, Departure_Date, Arrival_Date ON 

Booking
FOR EACH ROW
BEGIN
INSERT INTO Flight VALUES (:new.Aircraft_ID, :new.Departure_Date);
INSERT INTO Flight VALUES (:new.Aircraft_ID, :new.Arrival_Date);
END;