(To). To bamboozle, to deceive; to be in a quandary. “I am regularly flummuxed” —i.e. perplexed. The first syllable is probably a variant of flam, humbug, deception, and the word seems to be compounded on the model of the word “perplex.”
For the privates, the sergeants, and 'spectors, She flummuxed them all to a coon.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894