They can...but not far. There was a video showing them flying. I watched it a couple years back.
They fly in my backyard
Looking for a vegetable garden to raid
Wild turkeys can fly a pretty good distance, actual flying and not just gliding. In N.Fla many years ago I was on Hwy 20 probably 20 miles west of Tallahassee and 3 wild turkeys flew across the road, level flight and they were moving pretty fast. Came out of the trees on one side and disappeared into trees on the other side, at least 40 yards, which was just the part I saw.