Green’s Dictionary of Slang

sly, roguish, cunning [cite 1892 seems to suggest the oppsoite].

1844		New Sprees of London 25: There are plenty of flymy kids there, looking out for flats; so keep your ogles open.
1855		Yokel’s Preceptor title page: A Joskin’s Vocabulary Of the Various Slang Words now in constant use [...] all the New Moves and Artful Dodges practised at the present day, in all the most notorious Flymy Kens and Flash Cribs of London! [Ibid.] 29: Flymy, Down to everything – a man who has experienced life in all its stages.
1864, 1867, 1870		Hotten Sl. Dict.
1885		Bulletin (Sydney) 7 Mar. 13/1: What! You going to the Soudan, Flymy Billy; how’s that?
1887		W.E. Henley ‘Villon’s Good-Night’ in Farmer Musa Pedestris (1896) 174: You sponges miking round the pubs, / You flymy titters fond of flam. [Ibid.] ‘Culture in the Slums’ 179: Now ain’t they utterly too-too / (She ses, my Missus mine, ses she), / Them flymy little bits of Blue.
1892		E.W. Rogers [perf. Marie Lloyd] G’arn Away 🎵 Just because I’m a flimy girl yer takes me for a Jay.