The mouth of Sauron has spoken

[Anomalocaris]

Also the chance that an 88mm flak can take down a single aircraft/bird was slim.   It was a barrage weapon effective mainly against formations of aircraft that can’t maneuver.     Adding surface to air missiles would destroy the mystique of middle earth, to say nothing of the fact that what had not been known to Tolkien would remain forever unknown even to the valar.