Does my children needs id to flight domestic

Now, if both parents are traveling ok, but I know of people that have traveled alone with one child under 13 and they asked for consent from the other parent. But generally speaking no.

They have never asked for it before. Some of the airlines say you need a birth certificate but we have never been asked to show one

Not If they are with you.

No as long they are with you. If they are under 13 and alone yes.

Not if they are under 16