Green’s Dictionary of Slang

flattie n.1

also flatty
[flat n.2 (1)]

1. a dupe, a naïve countryman.

[UK]Hotten Dict. of Modern Sl. etc.
[UK](con. 1840s–50s) H. Mayhew London Labour and London Poor I 218/2: For they betray to the ‘flatties’ (natives) all their profits and proceedings. [Ibid.] 406: It was only 4s. or 5s., but then I was only a flatty or I could have made 14s. or 15s. at least.
[UK]Sl. Dict.
[UK]Leicester Chron. 6 Nov. 9/1: She’s an out an’ out ‘flatty’.
[UK]W. Newton Secrets of Tramp Life Revealed 9: Flatty ... One who does not understand the Cant.
[US]Tacoma Times (WA) 28 Dec. 3/6: ‘But I can’t get the fist,’ objected Jim. ‘Practice it, you flatty!’.
[UK]J. Ware Passing Eng. of the Victorian Era.
[UK]P. Baker Fabulosa 292/1: flatties [...] 2. dupes.

2. (Polari) a man, esp. as a member of an audience.

[UK]P. Baker Fabulosa 292/1: flatties noun: 1. men (especially those who make up an audience).
[UK]R. Milward Man-Eating Typewriter 121: [F]elching the trummuses of those destestable arroganki gillies and flatties.

In compounds

flatty-cop (n.) [cop n.1 (1)]

(Und.) a policeman who lacks sophistication in dealing with the underworld; a country policeman.

[UK]Leaves from Diary of Celebrated Burglar 18/1: The ‘flatty cops’ took in hand to hunt up Jem and Kay, whom they heard, from those around, were the parties implicated.
[US]Memphis Dly Appeal (TN) 12 Mar. 3/3: The police are generally known as ‘flatty cops’.
Emporia Dly Repub. (KS) 28 Apr. 3/2: A ununiformed officer is a ‘flaty [sic] cop’.
[US]A. Stringer Door of Dread 53: ‘Well,’ sez the flatty, showin’ his badge [...] ‘I’m goin’ to gather yuh in, and I’m goin’ to do it right now!’.
[UK]Thieves Slang ms list from District Police Training Centre, Ryton-on-Dunsmore, Warwicks 4: Flatty or flatty cop: Uniform policeman.
flatty-ken (n.) [ken n.1 (1)]

a public house that is frequented by members of the underworld but where the landlord remains oblivious of their activities.

[UK]Hotten Dict. of Modern Sl. etc.
[UK](con. 1840s–50s) H. Mayhew London Labour and London Poor I 243/2: ‘Flatty-kens,’ that is, houses the landlord of which is not ‘awake’ or ‘fly’ to the ‘moves’ and dodges of the trade.
[Aus]Melbourne Punch ‘City Police Court’ 3 Oct. 234/1: The Mayor.– Well my flying sawney hunter [...] you were reported to me as being scammered with some multee kertever flue fakers in a flatty ken.
[UK]Hotten Sl. Dict.
[Aus]Crowe Aus. Sl. Dict. 29: Flatty Ken, a publichouse whose landlord is ignorant of the habits of the thieves and tramps.