Flimflam is when someone plans a complicated scheme for tricking people out of their property or money. Some persons spell it this way "flim flam". Many flimflams are some version of a con, or "confidence game," in which the con artist first gains the trust or confidence of the victim, and then swindles money from him/her.
The most common form of this crime involves confusing a store cashier by trying to change large denomination notes and swapping money back and forth, until the cashier loses track of the transactions — and a bunch of money.