Truthfully, it's more his position as monarch of Wakanda that makes him so uber-rich. As the reigning monarch, where he much defend his crown periodically, he is responsible for the protection of his country's vibranium reserves. Wakanda has more of that than anyplace else on earth - even the Savageland. As vibranium is insanely expensive and the demand is outrageously high, they can name their price as well as their customer base.
That aside, Wakanda's technological might and reclusiveness make it a country to be reckoned with. They are generations ahead of the rest of the world and also make a substantial amount of money in its tech patents.
While the Black Panther is not personally rich, it's good to be the king.