Old English flowan "to flow, stream, issue; become liquid, melt; abound, overflow" (class VII strong verb; past tense fleow, past participle flowen), from Proto-Germanic *flowan "to flow" (cognates: Middle Dutch vloyen, Dutch vloeien, vloeijen "to flow," Old Norse floa "to deluge," Old High German flouwen "to rinse, wash"), probably from PIE *pleu- "flow, float" (see pluvial). The weak form predominated from 14c., but strong past participle flown is occasionally attested through 18c. Related: Flowed; flowing.

mid-15c., "action of flowing," from flow, v.. Meaning "amount that flows" is from 1807. Sense of "any strong, progressive movement comparable to the flow of a river" is from 1640s. Flow chart attested from 1920 (flow-sheet in same sense from 1912). To go with the flow is by 1977, apparently originally in skiing jargon.