flat (adv.)
1550s, "absolutely, downright;" 1570s, "plainly, positively," from flat (adj.). Flat-out (adv.) "openly, directly" is from 1932, originally in motor racing, picked up in World War II by the airmen; earlier it was a noun meaning "total failure" (1870, U.S. colloquial).
flat (v.)
c. 1600, "to lay flat;" 1670s in music, from flat (adj.). Related: Flatted; flatting.
flat (adj.)
c. 1300, "stretched out (on a surface), prostrate, lying the whole length on the ground;" mid-14c., "level, all in one plane; even, smooth;" of a roof, "low-pitched," from Old Norse flatr "flat," from Proto-Germanic *flata- (source also of Old Saxon flat "flat, shallow," Old High German flaz "flat, level," Old High German flezzi "floor"), from PIE root *plat- "to spread."

From c. 1400 as "without curvature or projection." Sense of "prosaic, dull" is from 1570s, on the notion of "featureless, lacking contrast." Used of drink from c. 1600; of women's bosoms by 1864. Of musical notes from 1590s, because the tone is "lower" than a given or intended pitch. As the B of the modern diatonic scale was the first tone to be so modified, the "flat" sign as well as the "natural" sign in music notation are modified forms of the letter b (rounded or square).

Flat tire or flat tyre is from 1908. Flat-screen (adj.) in reference to television is from 1969 as a potential technology. Flat-earth (adj.) in reference to refusal to accept evidence of a global earth, is from 1876.
flat (n.)
1801, "a story of a house," from Scottish flat "floor or story of a house," from Old English flett "a dwelling; floor, ground," from Proto-Germanic *flatjam, from suffixed form of PIE root *plat- "to spread." Meaning "floor or part of a floor set up as an apartment" is from 1824. Directly from flat (adj.) come the senses "level ground near water" (late 13c.); "a flat surface, the flat part of anything" (1374), and "low shoe" (1834).