Where did the phrase-four flusher-originate?

Answer 1

Cards, specifically poker. A four flusher would show his hand in such a way that only four of the cards showed fully, but would claim to have a flush.

Answer 2

From poker.

Five cards of the same suit (a flush) is a strong hand that usually wins. Four cards of the same suit (a four card flush, or "four flusher") is worthless.

It's more pertinent to the game of five card stud, where one card is dealt face down and four cards are dealt face up. With all four up cards being the same suit, the hand appears to be very strong, even though there's only about a 25% chance the hole card is of the same suit. The player often bluffs that he has a flush even when he doesn't have the hole card to back him up.