“She maketh earnest matter of euery flymflam,” was listed as one of the Prouerbes in the Englishe tongue, compiled by John Heywood in 1546.
So the word “Flimflam” must be considerably older than that date, the earliest in recorded print.
It had no known source, except that it seems to have been a reduplication, for added effect, on Elam, “a whim,” “a falsehood,” or just “nonsense.”