First we'll perform a small refactoring and extract the seat designator parsing and validation logic into it's own method, _parse_seat(). We use a leading underscore here because this method is an implementation detail:

class Flight:

    # ...

    def _parse_seat(self, seat):
        """Parse a seat designator into a valid row and letter.

        Args:
            seat: A seat designator such as 12F

        Returns:
            A tuple containing an integer,string for row and seat.
        """
        row_numbers, seat_letters = self._aircraft.seating_plan()

        letter = seat[-1]
        if letter not in seat_letters:
            raise ValueError("Invalid seat letter {}".format(letter))

        row_text = seat[:-1]
        try:
            row = int(row_text)
        except ValueError:
            raise ValueError("Invalid seat row {}".format(row_text))

        if row not in row_numbers:
            raise ValueError("Invalid row number...