Green’s Dictionary of Slang

fly n.⁴

a spree, a ‘lark’.

1889		‘’Arry in Switzerland’ in Punch 5 Dec. in P. Marks (2006) 98: Think I / Slippin’ ’ome I’ll take France on the way, and go in for a bit of a fly.
1890		‘’Arry on the ’Oliday Season’ in Punch 16 Aug. 75/1: Can’t yer jest turn the tables, old hoyster, and come for a bit of a fly.

In phrases

on the fly

out on a spree; drunk.

1873

Sl. Dict.