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.
word-forming element making verbs (such as darken, weaken) from adjectives or nouns, from Old English -nian, from Proto-Germanic *-inojan (also source of Old Norse -na), from PIE adjectival suffix *-no-. Most active in Middle English and early modern English, hence most verbs in -en are comparatively recent.