Do wealthy americans pay for public schooling?

Well, their property taxes contribute to their local schools, so, YES.

Their houses are likely much more expensive than the houses of middle class or poorer people, so they probably pay a disproportionate amount.

Depending on the area it is, I would assume a good portion of the children of the rich go to private schools as opposed to the public school, so the rich pay, but don't use hte service, so that is a factor to consider when judging their contribution.