c. 1300, "a smell, odor" (usually a pleasing one), from Old French flaor "smell, odor; action of smelling, sense of smell," probably from Vulgar Latin flator "odor," literally "that which blows," in classical Latin "blower," from flare "to blow, puff," from PIE root *bhle- "to blow."
"Not common before Milton's time" [Century Dictionary], and it is not clear what exactly Milton meant when he used it. The same Vulgar Latin source produced Old Italian fiatore "a bad odor." Sense of "taste, savor" is 1690s, perhaps 1670s; originally "the element in taste which depends on the sense of smell." The -v- in the English word is euphonic or perhaps from influence of savor. Flavor-of-the-month is from 1946 (originally of ice cream).