Here is a picture of my son carrying a hen on his shoulders, as he does frequently. She doesn't flap, peck or fuss. They walk together around the property like this. Should I discourage this? Is he hurting her?
It is difficult to be sure from the photo angle, but IMO if he is holding her by her legs/feet there is a risk of injury to her. If you haven't already done so, watch to see how she acts when he picks her up. If she demonstrates distress initially, she may just be submissive and not really enjoy this or be passive with fear.
You should explore how to catch and carry a chicken for comparison.