Green’s Dictionary of Slang

flat adj.1

[opposite of sharp adj. (1)]

naïve, unsophisticated.

[UK]R. Armin Nest of Ninnies 12: All such, say I, that use flat foolerie, Beare this, beare more; this flat foole’s companie.
[UK]J. Taylor ‘A Kicksey Winsey’ in Works (1869) II 39: No wiser than flat fooles they be.
[UK]G. Stevens ‘A Fore-Castle Song’ Songs Comic and Satyrical 96: Odd Lingos Musicians write in, / Concerning Flats, Sharps, and all that; / We Seamen are sharp in our fighting, / And as to the Frenchmen they’re flat.
[UK]‘T.B. Junr.’ Pettyfogger Dramatized I vi: Blast me, i’m flat—dam’me, ’tis all my eye, Betty Martin.
[UK]P. Egan Key to the Picture of the Fancy going to a Fight 7: A young man of nineteen, who has been flat enough to lay the man of colour [i.e. ex-slave-turned-prizefighter Bill Richmond], that ‘he is an ancient Briton!’.
[UK]J. Thomson An Uncle Too Many I ii: Famous! if he is but flat enough to believe it.
[UK]Satirist (London) 10 May 501/3: ‘If they had not been flat fish do you think they would have come near the hook?’.
[US]J.C. Neal Charcoal Sketches in Schele de Vere Americanisms (1871) 602: Not to hurt a gentleman’s feelings and to make him feel flat afore the country .
[UK] ‘Characters of Freshmen’ in Whibley In Cap and Gown (1889) 176: The Flat Freshman [...] putteth his cap on the wrong way.
[UK](con. 1840s–50s) H. Mayhew London Labour and London Poor I 310/2: The place was well-known to the monkry, and you was reckoned flat if you hadn’t been there.
Sydney Sportsman (Surrey Hills, NSW) 6 Nov. 4/2: [of a pak-a-pu ‘parlour’] he manager of the joint [...] has placed before him a list of every combination marke ooff by the flat investors.

In compounds

flat fish (n.) (also regular flat fish) [fish n.1 (4); or ? just a simple joc. use of SE]

1. a fool, a dullard.

[Ire]J. O’Keeffe Wild Oats (1792) 49: You’d disgust her, you flat fish.
[UK]C.M. Westmacott Eng. Spy II 368: Meer Cyprian traders, captain, from the Gulf of Venus, engaged in gudgeon hawling, or on the look-out for flat fish.
[UK] ‘Catalogue of Odd Fish’ in Fleet-Street Collection 8: We shouldn’t miss much of [off?] the mark, / If we set down the clients as flat fish.
[US]J.C. Neal Peter Ploddy and Other Oddities 149: A werry flat sort of a fish, that chap is.
[US]‘Hugh McHugh’ Back to the Woods 13: I made up my mind one day I’d run down to the Flatfish Factory and drag a few honest dollars away from the Bookmakers.

2. a beggar’s or confidence trickster’s prey.

[UK] letter in Times 8 Dec. n.p.: The invunerability of ‘Fishmonger’s Hall,’ or the Crock-odile Mart for gudgeons, flat-fish, and pigeons, is likely soon to be put to the proof.
[UK] ‘Life of a Vagabond’ in Holloway & Black II (1979) 63: On flatfish I contrive to live though some call me a shark.
[UK]J. Greenwood Seven Curses of London 407: This is the way Dodger angles for ‘flat-fish’ of tender age.

3. a prostitute.

[UK]‘Randy Mots of London’ in Libertine’s Songster in Spedding & Watt (eds) I 139: The fishmonger’s a friskly blade, / And though he dearly likes a maid, / For any flat-fish he’s the blade, / And thinks he’s not by one done.