[winged insect] Middle English flie (2), from Old English fleoge, fleogan "a fly, winged insect," from Proto-Germanic *fleugon "the flying (insect)" (compare Old English fleogende "flying"). According to Watkins this is from PIE root *pleu- "to flow," which is also the reconstructed source of fly (v.1). The plural flien (as in oxen, etc.) gradually was normalized 13c.-15c. to -s.
Originally and in popular language a flying insect of any common kind (moths, gnats, bees, beetles, locusts, hence butterfly, etc.) and long used by farmers and gardeners for any insect parasite. Especially of the common house-fly (Latin musca). In modern entomology, a two-winged insect of the order Diptera especially of the family Muscidae.
Flies figuratively for "large numbers" of anything is from 1590s. Fly in the ointment "small or trifling matter which spoils enjoyment" is from Eccles. x:1. Fly on the wall "unseen observer" is recorded by 1881. No flies on _____ "no lack of activity or alertness on the part of," is attested by 1881, said to be a reference to active cattle.
The meaning "fish-hook dressed to resemble an insect" is attested from 1580s; fly-fishing is from 1650s; fly-rod, used by anglers in fly-fishing, is from 1680s.
The fly agaric mushroom (1788) is so called because it was used in fly powders and other poisons for flies.
Germanic cognates include Old Saxon fleiga, Old Norse fluga, Middle Dutch vlieghe, Dutch vlieg, Old High German flioga, German Fliege "fly."