Who owns uninhabited islands?
No doubt someone would have discovered this island before you, the country to discover the island owns it first. If you were the first person to discover an island (although, probably every island has been discovered), it would be a little complicated. Depending on where you discovered this island you might get to keep it. for example; if you discovered this island in the China sea, China would take it right off you, because it’s in their territory. If you discovered this island in no territory it is yours to keep, and to be a king of your island it would have to be a country, no doubt you will be refused that. So, no, you could not become a king of your nation if you discovered an island.