Especially if you recognize your car's history (or lack of history) on the previous page, an engine flush could help keep your new oil clean. That's why these services are often performed together: First the flush to get rid of old oil deposits, then the new oil to keep the engine in tip-top shape.
Without the engine flush, the new oil will just pick up the old deposits and sludge and keep them circulating through the engine. Soon enough, the new oil is just as dirty as the old oil. An engine flush can help you go longer between oil changes, especially if the maintenance on the car hasn't been perfect.