E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Flummux (To).
To bamboozle, to deceive; to be in a quandary. I am regularly flummuxedi.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.