Place potato slices in a bowl of water while preparing remaining ingredients.
Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch baking dish with cooking spray.
Melt butter in a saucepan over medium heat; cook and stir flour in melted butter for 2 to 3 minutes. Stir in milk until thickened, 4 to 5 minutes more. Add American cheese, mixing until melted. Pour in jarred cheese sauce and cook and stir until smooth.
Spread about 1/2 cup sauce in the bottom of the prepared baking dish. Layer potatoes slices in baking dish, alternating with cheese sauce.
Bake in preheated oven until potatoes are tender, about 90 minutes.