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).
-ful
word-forming element attached to nouns (and in modern English to verb stems) and meaning "full of, having, characterized by," also "amount or volume contained" (handful, bellyful); from Old English -full, -ful, which is full (adj.) become a suffix by being coalesced with a preceding noun, but originally a separate word. Cognate with German -voll, Old Norse -fullr, Danish -fuld. Most English -ful adjectives at one time or another had both passive ("full of x") and active ("causing x; full of occasion for x") senses.
It is rare in Old English and Middle English, where full was much more commonly attached at the head of a word (for example Old English fulbrecan "to violate," fulslean "to kill outright," fulripod "mature;" Middle English had ful-comen "attain (a state), realize (a truth)," ful-lasting "durability," ful-thriven "complete, perfect," etc.).