Phlegm
Middle English fleem, fleume, from Old French fleume, from late Latin phlegma ‘clammy moisture (of the body)’, from Greek phlegma ‘inflammation’, from phlegein ‘to burn’. The spelling change in the 16th century was due to association with the Latin and Greek.
wiktionary
From Middle English flewme, fleume, fleme, from Old French fleume, Middle French flemme (French flegme), and their source, Latin phlegma, from Ancient Greek φλέγμα(phlégma, “ flame; inflammation; clammy humor in the body”), from φλέγειν(phlégein, “to burn”). Compare phlox, flagrant, flame, bleak(adjective), fulminate. Spelling later altered to resemble the word's Latin and Greek roots.
etymonline
phlegm (n.)
late 14c., fleem, fleume, "viscid mucus, discharge from a mucous membrane of the body," also the name of one of the four bodily humors, from Old French fleume (13c., Modern French flegme), from Late Latin phlegma, one of the four humors of the body, from Greek phlegma "morbid, clammy bodily humor caused by heat;" literally "inflammation, flame, fire, heat," from phlegein "to burn," related to phlox (genitive phlogos) "flame, blaze," from PIE *bhleg- "to shine, flash," from root *bhel- (1) "to shine, flash, burn."
The modern form of the word is attested by c. 1660. In old physiology it was the "cold, moist" humor of the body and a predominance of it was believed to cause dullness, lethargy, and apathy, hence phlegmatic.