Flushing

mid-13c., flusshen "move rapidly or violently; rush, dart, spring" (intransitive); late 15c., flush up, transitive, "cause to fly; start or flush (birds)," perhaps imitative of the sound of beating wings.

The sense of "spurt, rush out suddenly, flow with force" (1540s, usually of water) probably is the same word, with the connecting notion being "sudden movement," but its senses seem more to fit the older ones of flash (v.), now all transferred to this word except in flash flood, via its variant flushe. OED considers this probably not connected to Old French flux. Transitive sense "cause to flow" is from 1590s.

Meaning "cleanse (a drain, etc.) with a rush of water" is from 1789. Of the face, "become suffused with warm color," from 1680s (flushed). Sense of "inflame with pride or passion" as a result of success, victory, etc., is from 1630s; perhaps influenced in sense by flesh (v.). Related: Flushed; flushing.