Slang usage of "fish" meaning US Dollar.
'Fish' as chips
J.E. Lighter, Random House Historical Dictionary of American Slang (1994) traces fish in the sense of "a dollar" to 1917, but finds a related sense that goes back almost 200 years earlier:
fish n. {[from] F[rench] fiche} 1. Gamb[ling] a counter or chip used in wagering Orig[inlly] S[tandard] E[nglish].
Harrap's New Collegiate French and English Dictionary (1978) gives three basic meanings for the noun fiche:
fiche, s.f. 1. Peg, pin (of iron, wood); stake. ... 2. (a) Slip (of paper); memorandum slip; voucher. ... (b) Card, ticket (of membership,, etc.) (c) Index card. ... (d) Tie-on label. 3. Cards: etc: Counter, marker; fish.
The first citation in Lighter for this gambling sense of the word is (via the OED) from John Vanbrugh & Colley Cibber, The Provoked Husband; or, A Journey to London (1728). Here is a longer rendition of that quotation:
Lord Townly. And I had rather it should be so, madam [that she should gamble away the 500 guineas he has just given her]; provided I could be sure that were the last you would lose.
Lady Townly. Well, my lord, to let you see I design to play all the good housewife I can, I am now going to a party at quadrille, only to trifle with a little of it, at poor two guineas a fish, with the duchess of Quiteright. [Exit. Lady Townly.
The next instance (also quoted from the OED) is dated to 1816, but appears also in The Humorist: A Collection of Entertaining Tales, Anecdotes, Epigrams, &c. (1892):
Flat Fish.
A notorious gamester having, at a game of loo, accumulated a large quantity of fish before him, an opponent observed that he had got so much he might commence fishmonger. A bystander dryly remarked, "Yes, he may, but his dealings are confined to flat fish."
Without any help from the OED, Lighter finds examples from T.L. Clark, Dictionary of Gambling (1836), evidently describing how to play the game of Boston, a variant of whist:
The players put eight counters or fish into the pool, and dealer four additional.
and from George Matsell, Vocabulum or the Rogue's Lexicon (1859):
CHIPS or CHECKS The chips or checks are round fancy pieces of ivory about the size of a half dollar, and a trifle thicker. These represent money, and are received from the dealer to play with in exchange for money. They are much easier to handle, and the dealer can see at a glance how much money is bet on a card. The color of the chips indicate the value they represent. There are three colors, namely, red, white, and blue. White chips represent twenty-five cents, or one dollar, according to the house. Red chips represent five times the value of the white chips. Blue chips represent $25, $50, and $100. A hundred dollar chip is the highest "fish," as the gambler calls it.
So chips were fish and represented money. Under the circumstances, it's not hard to imagine how fish came to mean money itself.
'Fish' as dinero
Lighter's first match for fish in the sense of money is from Logan Ruggles, The Navy Explained (1917) [no preview]:
Three hundred fish for me at the end of this hitch.
And his second is from Our Navy (December 1919):
Funny Government we have. After doing your bit, they turn you loose with a $60.00 bonus to buy your entire outfit of clothing with. You need a suit to get a job in, but the sixty ducats just about buys a collar button these days. They set you back ten fish for a lid and charge you war tax on in to cover the war you helped win.
If the money sense of fish in U.S. slang arose during World War I, it's possible that it was pushed along by a second round of exposure to the French fiche. (That might also explain the coincidence that Lighter's two earliest citations for fish as money come from U.S. Navy sources.) But whether fiche had any renewed influence on the evolution of fish or not, the jump to that meaning was only a bunny hop away from the longstanding meaning of fish as gambling chips or checks.