This game, a relative of Barbu, is played in various parts of the world. It is known in France, Belgium and Italy and is particularly popular in Portugal, Russia, Turkey, Colombia and Brazil. In all these places it is known by the English name King as well as by a variety of local names. This leads people to believe that the game comes from England, but it never appears in English language card game books and I know of no evidence that it has ever been played in any English speaking countries. It is quite mysterious why this game should bear an English name, as well as how it has come to be popular in such widely separated parts of the world.
Rules of various versions of King will be explained and compared on this page eventually. Meanwhile here are some links.
You can download a freeware King program from Thanos Card Games.