Is kentucky the state that was not one of the original thirteen colonies?

No. Kentucky was part of the trans- Allegheny area that was ceded to the United States in the treaty of Paris. As the country started to move westward it became part of the overflow of people and settled by families and farms. It will become a state within 13 years after the establishment of the United States. Kentucky and Tennessee became a place for people like Daniel Boone( for a short time) to escape to and to get away from cities and people/farms that were taking over.