I flew about 10 days after my hair transplant, and it went pretty smoothly. I made sure to follow all the post-op care instructions, like avoiding touching my scalp and wearing a hat to protect it from the sun. The only issue I had was some swelling during the flight, but it went down once I landed.
I would recommend waiting at least a week before flying to give your scalp some time to heal. Plus, sitting on a plane for an extended period of time can be uncomfortable right after surgery. Just make sure to check with your surgeon for their specific recommendations based on your individual situation.