Kemsing is an Old English ing, or place, associated with someone called Cymesa. It is first recorded in 822 as Cymesing.
Kenardington is also an eponymic, this time suggesting an Old English tun farmstead, village connected with a man called Cyneheard. The middle element is Old English ing, denoting simply a place. It first shows up on record as Kynardingtune in the eleventh century.
Kennington unlike its namesake in Greater London is literally a royal manor, from the Old English cyne royal (from cyning king) and tun estate, manor. It first shows up in the Domesday Book as Chenetone.
Kindsdown, near Deal, and West Kingsdown both look back to Old English cyning king and dun hill, and thus denote the Kings hill. The latter appears first on record as Kingesdon in 1199; the former in 1318 as Kyngesdoune.
Kingsgate has one of the most directly historical place-names in Kent: it was at this gate, or gap in the cliffs, that Charles II landed in 1683.
Kingsnorth has nothing etymologically to do with North as a compass direction. It goes back to Old English snad, used to denote a detached piece of land or woodland. Here the sense is of a detached piece of land belonging to the King, and it first shows up on record in 1226 as Kingesnade.
Knockholt is etymologically a town at an oak wood, from the Old English ac oak and holt woodland. It first appears as Ocholt in 1165; it acquired an initial N- from the Old English definite article (appearing as Nocholt by 1353).
Knowlton is literally a farmstead by a hillock. It comes from Old English cnoll hillock, knoll and tun farmstead, settlement. Its first recorded form, from the Domesday Book, is Chenoltone.