Wild Turkeys do fly. Just usually not very far, and usually only to escape predators or to fly into trees at night. Or to fly onto my roof to get the the yard on the other side of my house lol
I saw one fly across a road once. It broke my brain until I recognized what it was. Initially I thought it was a leather satchel being blown by the wind like a plastic bag in an updraft. Not exactly a graceful display.