As John-John Kennedy had no children, the grant of arms, which was made to his late father in 1963, ceases to have effect. He goes to his watery grave this Thursday taking a bit of Irish heraldic history with him. There is no such thing as a family coat of arms. A coat of arms is the property of a person, and it passes in direct descent upon the death of its owner. It is possible that the right to the coat of arms might pass to John-John's sister, Caroline, although I'm not sure if that would be the usual thing.
Coats of arms are rather precisely defined affairs.
There is an entire nomenclature to describe them. In the case of bishops, and the like, they get an heraldic device upon their appointment. In the case of towns, counties, cities, universities, etc, the coat of arms is a permanent symbol, often used as little more than an industrial logo for promotional purposes. Simple-there was no means by which the country could have honoured him otherwise. With Israel, we have an absolute prohibition in our Constitution against the State granting titles of honour.