flux (n.)

The section of entries for the various flushes in Century Dictionary opens with a caveat:

The several words spelled flush, being mostly dialectal, colloquial, or technical, and scantily recorded in early literature, have become partly confused with one another, and cannot now be entirely disentangled. Words originally different have acquired some meanings very nearly identical, while on the other hand there are some meanings not obviously related which are, nevertheless, to be referred to one original.

Weekley calls it "A very puzzling word." Sense of "a rush of water" in a stream (1520s), is probably from flush (v.1). From this likely come the extended senses "rush of emotion or passion" (1610s); "a sudden shooting up" (1773); "act of cleansing (a drain) by flushing" (1883); "glow of light or color" (especially sudden redness in the face), 1620s. Independently from the verb, probably, is the noun sense of "a flight of birds suddenly started up" (1590s).

The meaning "hand of cards all of one suit" (1520s) is of uncertain origin, perhaps formed on the model of French flus (15c.), from Old French flux, flus "a flowing, rolling" (see flux), which, in common with its Italian cognate flusso, is said to have once had a sense of "a run" of cards. The form in English probably was influenced by flush (v.1).