'flunk' originates from American English (student slang), first recorded around the turn of the 20th century; it is likely imitative/colloquial in origin rather than derived from a classical root.

'flunk' appeared in U.S. student slang (c. 1900) meaning 'to fail'; it then entered wider American English usage with the same sense and produced derived forms such as 'flunked' and 'flunking'.

Originally associated with an imitative sense (a dull fall or failure), it came to be used specifically for 'failing an examination or course' and related senses.