“The swell was flash, so I could not draw his fogle.”
Swell: gentleman (1811 Dictionary of the Vulgar Tongue by Francis Grose)
Flash: Knowing. Understanding another’s meaning. (1891 American Slang Dictionary by James Maitland)
Draw his fogle: pick his pocket of his silk handkerchief. (1891 American Slang Dictionary by James Maitland)
In other words: the gentleman knew exactly what I was doing so I could not sneak the silk handkerchief from his pocket.