"Place your hand around the neck of the bottle, so that your hand is flush to the top". From WikiHow.
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."