Who will inherit?

AFAIK, a vassal needs to be of lower rank than his liege.

That is, if the lad inherits a kingdom, that kingdom will be his primary title. He may become a vassal of whichever empire that kingdom belonged to, but he will not become your vassal by virtue of inheriting or having inherited a minor title from your domain.

In fact, it is possible that the duchy may become part of his kingdom. I've had that happen, though you might possibly be able to avert that by passing appropriate realm laws (the particulars will vary depending on game version).

If you want him to become your vassal, you have to be liege of his primary title. That is, you will need to be emperor, and make sure that the first kingdom he inherits is in your empire.

If your goal is to politically merge the kingdoms, you may want to try making the lad your heir.

The accepted answer is not 100% correct. Also the question in itself does assume a thing that is not true. As long as the child of your vassal duchess and the foreign king does not have any land on his own he is not considered your vassal, only part of your court.

Besides that, if we assume that the child is the sole heir of both, your duchess and the foreign king, the order of the deaths play a big role. Consider following:

If the foreign king dies, the child will inherit his kingdom title and instantly be either an independent king of himself or a vassal of another emperor, which was the liege of the deceased king. His mother still holds a duchy in YOUR kingdom and therefore is still your vassal. If your mother then dies, your kingdom rules play a big role. If you have rules enacted to forbid outsider to inherit realm titles (legalism 4 is needed for that rule to be enabled) the next in line will inherit, NOT the new king. Otherwise, the duchy will be plucked out of your realm and added to his kingdom.

Now, if your duchess dies first, the child will inherit her duchy, and because she was your vassal, he will be your vassal (since the title is part of your realm). When the king dies afterwards, their will be no rule which will stop this child from going independent from you (with your duchy) since his title is the same rank as yours and it is not possible for kings to have vassal kings.

My suggestion, if you really want to keep the duchy in your realm, either try to make that child your heir aswell (so you'll get both kingdoms) or try to rip the duchess of of her title and award the title to someone else.