Green’s Dictionary of Slang

(US campus) one who fails an examination; thus one who is expelled as a result of this; Hall (1856) does not support De Vere’s idea of ‘backing out’ of an exam; the definition is simply that of failure.

1854		Yale Literary Mag. xx 76: I am a college pony, Coming from a junior’s room; / I bore him safe through Horace and saved him from a flunkey’s doom.
1872		Schele De Vere Americanisms 603: Flunky, in college parlance, means the man who backs out from recitation or examination for fear of failure; while in the slang of Wall-street it denotes the unlucky outsider who ventures to speculate in stocks without the necessary knowledge of monetary matters.
1915		M.G. Hayden ‘Terms Of Disparagement’ in DN IV:iii 202: flunky, one who fails.
1924		P. Marks Plastic Age 111: Some of the flunkees took the news very casually, packed their trunks, sold their furniture, and departed.
1957		H.S. Thompson letter 3 Mar. in Proud Highway (1997) 45: The list of flunkees and potential flunkees is imposing.
1967–8		Baker et al. CUSS 119: Flunky A person without much social or academic ability.