結合を行うときにテーブルにエイリアスを設定します:
SELECT
flight.idflight,
flight.idairline,
flight.from_airport,
flight.to_airport,
flight.number,
airport_from.name AS origin
airport_to.name AS destination
FROM flight
INNER JOIN airports airport_from ON flight.from_airport = airport_from.idairports
INNER JOIN airports airport_to ON flight.to_airport = airport_to.idairports