"Place your hand around the neck of the bottle, so that your hand is flush to the top". From WikiHow.
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It means "even with the top." In other words, imagine your hand and the bottle pressed against the underside of a table. If your hand is flush with the top, then both the top of your hand and the top of the bottle would be touching the undersurface with a relatively equal amount of pressure.
My online dictionary lists one definition of flush as "completely level or even with another surface."