Precursors of the Flushtration Count concept with cards were performed with coins and poker chips. In the original Tarbell Course in Magic from 1926, Lesson 37 opens with the “Chinese Color-Changing Coins.” Tarbell proclaims that it is “real Oriental magic,” but offers no provenance. The handling does not actually use the Flushtration Count per se, but comes awfully close when the top and bottom coins in a stack are displayed to give an impression that all sides of all the coins are the same color.
In the mid-1930s Percy Abbott marketed the same trick as "Abbott’s Chinese Coins Magic”, and stated that he’d learned it in China years earlier. Later ads said the instructions were written and illustrated by Harlan Tarbell. This trick did not appear in the original six revised volumes of the Tarbell Course. However, in 1993, an eighth volume of the Tarbell Course was published, containing material from the original course and other sources, much of which had been rewritten by Tarbell prior to his death in 1960. The revised write-up for the “Chinese Color-Changing Coins”, p. 115, states that it was taught to Tarbell by Abbott and claiming that the latter learned the trick while in China in the very early twentieth century. That said, nothing along these lines has been discovered to date in any Asian magic texts.
The Flushtration Count principle does appear full-blown in 1956, done with a stack of three poker chips. See “Christopher's Chip Trick” in Walter Gibson's What's New in Magic, p. 168.
While often credited to Bro. John Hamman, this false display with a packet of cards was first described in print by Norm Houghton in Ibidem, No. 1, June 1955, p. 8. Houghton prefaces the display – which isn't a straight Flushstration Count – by referring to the central concept of showing a back or face repeatedly as several different cards as being an “old principle.” The “old principle” he referred to was later identified by Ariel Frailich in a footnote in Houghton's Wit and Wizardry, 1998, p. 55, as Harris Solomon's Hindu Shuffle False Display, published in his trick “Nomolos” in The Jinx, No. 44, May 1938, p. 301. It is easy to see that the Flushtration Count is indeed a packet adaptation of Solomon's procedure with a full deck.
Also see Hindu Shuffle False Display.