The kids are 3, 3, and 8.

There are many combinations of three numbers that have a product of 72, so of course Jack will need more information. After the second hint, Jack still does not know the answer. There are only two sets of ages that both have a product of 72 and add up to the same value: 2,6,6 and 3,3,8. All the other age sets have a unique sum – if it were one of these Jack would not need the third hint. By saying that there is an oldest child, Jack could eliminate 2,6,6.