Coolant flows from the engine block into the through the coolant jacket?

Kind of. There are water jackets inside the engine block and usually the heads of a liquid-cooled engine Water (or coolant) will either flow from the block to the head to the radiator, or from the radiator through the head to the block (a reverse flow design). The latter is better because it cools the heads first and helps prevent detonation. It also reduces thermal shock to the engine block.