" 'The overload shorted out the time circuits and destroyed the flying circuits. Unfortunately the car will never fly again.' It actually flew?"
1955 Doc reading aloud the letter his older self sent from 1885.

Flying circuits were part of a hover conversion job Emmett Brown had done to the DeLorean time machine in 2015. These enabled the car to fly, in addition to tires that rotated to provide upward thrust.

The DeLorean's flying circuits were unfortunately destroyed by a Jigowatt overload caused by it being struck by lightning on November 12, 1955, which in turn sent it and Doc back to 1885. Doc mentioned this in the letter he sent via several generations of Western Union to Marty McFly in 1955, which was delivered by one of their employees shortly after Marty saw the DeLorean vanish.