We don't let the kids chase the chickens for fun.
That being said, I chased chickens as a kid. Not ever to be mean, mind you. We had 30 odd free range bantams, and my brother, cousins and I would chase them down, catch them, and pet them. Then let them go. They were not really afraid at all, they just didn't really like it. You could tell they were calm about it because as soon as we had them, they just sat there, patiently waiting for us to get bored. We never hurt them, and my dad wouldn't have let us do it if we did. We also never chased too hard. We had enough that if one was really freaked out, or ran too fast, we would just catch a different one. On 1.2 acres with lots of shelter and no real corners, they could evade us if they tried... but I think we caught the same 5 chickens every day. One of which was our head rooster.