They can, but not like geese who fly long distances, or songbirds that fly all over, or raptors. Turkeys are more land based, but they fly up into trees to roost at night. Considerably high up, too. I was running early one morning when a turkey dropped fifty feet out of the tree next to me. Scared me silly.

Another time I was biking along a wooded road and scared up a hen turkey from the brush and she flew over my head up into a tree. I fell off my bike. They are much bigger in real life, and strong, and they can be nasty. Blocking traffic, pecking your cars, hassling you. Guinea hens are worse but if you see a mob of turkeys headed your way, hide.