Kensington Plantation is located near the confluence of the Black and Pee Dee Rivers on the north side of Georgetown, SC. I am not sure where the Kinloch Plantation you refer to is located, but Kensington is still referred to by its original name. It is currently being developed as a residential community.
Francis Kinloch (Sr.) founded Kensington in 1751, and it was willed to his son, Francis Kinloch (Jr.) upon his death. In the early 1800s, it was sold to Arthur Middleton (Kinloch's son-in-law). If you are interested in the history of the plantation (and of the Kinlochs), look at the "Historical Atlas of the Rice Plantations of Georgetown County and the Santee River" by Suzanne Linder and Marta Thacker (2001). If your local library doesn't have a copy, you should be able to get it by interlibrary loan.
Hope this helps,