Clipping the wings is about like clipping the nails of a child or a dog, or cutting the hair of a small child: they don't like having it done, but it does not actually hurt them, if you do it right. (I'm sure you know that clipping your own fingernails and hair doesn't hurt.)
Clipped wings do not completely prevent flying, but they make the chickens fly less well.
Clipped wings do not completely prevent flying, but they make the chickens fly less well.