It's not an analogy! It's another similar use of the word. As long as he's learning one more definition for the word flush, why not one more?
We should not forget that flush also refers to the time when a person's face becomes red.
As in, your face will go flush if you realize your credit card reader is not flush because you might have just flushed all your winnings from having a poker flush down the toilet.
Please keep comments constructive. This does not help the original questioner, who may not understand why it isn't a fantastic analogy. Please either refrain from the negative commentary, or enhance the conversation by clarifying why you feel it is lacking.
In this case the poker analogy is terrible because in this case flush is talking about a physical surface being unbroken while poker is talking about a collection of items all being the same.
Wouldn't that be a very similar meaning? An unbroken chain of cards of the same suit? Makes sense to me.
I think a flush in poker may have been more inspired by the sense of being full -- "flush with cash".