1540s, "spread out" (hair), of unknown origin, perhaps from Scandinavian or from Dutch vlederen. Meaning "shine out with a sudden light" is from 1630s. The notion of "spreading out in display" is behind the notion of "spreading gradually outward" (1640s). Related: Flared; flaring.
"a giving off of a bright, unsteady light," 1814, from flare (v.). This led to the sense of "signal fire" (1883). The astronomy sense is from 1937. Meaning "a gradual widening or spreading" is from 1910; hence flares "flared trousers" (1964).