c.1200, flutten "convey, move, take," perhaps from O.N. flytja "cause to fit," from P.Gmc. *flotojan (see float). First record of flitter, with frequentative suffix, is from 1542. Flitter-mouse (1547) is occasionally used in Eng., in imitation of Ger. fledermaus "bat," from O.H.G. fledaron "to flutter."
"Theire desire ... is to goe to theire newe masters eyther on a Tewsday, or on a Thursday; for ... they say Munday flitte, Neaver sitte." [1641]