The K.M. move was devised by Tony Kardyro and Ed Marlo, and jointly published in The K.M. Move, 1962, p. 2. It has its roots in the fingertip version of the slip cut. More directly, it has a predecessor in a move of Charles Jordan's in “Sympathetic Sympathy” from Four Full Hands of Down to the Minute Magical Effects, 1922, p. 27. Jordan would hold two packs of cards, and then pull the top card of the upper pack down to the top of the lower pack during a wrist kill. The K.M. Move uses the identical actions, but with two cards instead of two decks.
In 1928, William Larsen and Page Wright published a method for secretly reversing a card in the center of the deck, using a slipping action that can also be viewed as a precursor to the K.M. Move. See “A Double Reverse” in The L.W. Card Mysteries, p. 27.
Jean Irving's “Peek”—a method for reversing a peeked card in place in the center of the deck—appeared in The Phoenix, No. 70, Sep. 29, 1944, p. 286. This sleight is very similar to that described by Larsen and Wright, and may also be viewed as a relative to the K.M. Move.