Preheat oven to 375 degrees. Thinly slice (1/8-inch thick) potatoes and layer in a 9- by 13-inch pan coated with cooking spray. Top potatoes with onion rings and set aside.

In a large bowl, whisk together flour and water. Whisk in barbecue sauce, vinegar, salt, and pepper. Pour over potatoes, cover with foil, and bake for 1 hour; stir every 30 minutes.

Remove foil after 1 hour baking time, return potatoes to oven, and continue baking an additional 45 minutes or until potatoes are tender when pierced with a fork.