"Flush" in the poker context has more to do with definitions 1 (Abundantly full. In later use chiefly of a stream, etc.: Full to overflowing, swollen, in flood.) and 3 (Plentifully supplied (esp. with money).) rather than 5 (Even, level, in the same plane with / Even or level with the adjacent surface.).

To be "flush with money" is to have a lot of money---in poker, to be flush with hearts is to have 5 hearts.

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