Английский Этимологический словарь - flare (v.)

- c.1550, originally "spread out" (hair), of unknown origin, perhaps from Du. vlederen. The n. "bright, unsteady light" is 1814, from the verb. The notion of "spreading out in display" is behind the notion of "spreading gradually outward" (1644). Flares "flared trousers" is from 1964.