Fixing it - exactly like it was shown in your error message:
UPDATE `FlightSchedule` 
SET delay=
(SELECT update_field
 FROM 
 (
  SELECT MINUTE (ETA - STA) AS update_field
  FROM `FlightSchedule` 
  WHERE `flightNum_arr`='3517'
 ) AS internal_0
)
WHERE `flightNum_arr`='3517';
But actually above there more correct suggestion - get rid of that nested subquery at all (see Gordon's answer).
Edit (based on comments):
If you want to find difference, use TIMEDIFF function:
UPDATE `FlightSchedule` 
    SET delay = TIMEDIFF(ETA - STA)
    WHERE `flightNum_arr`='3517';