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';