Place chicken breasts between 2 sheets of heavy-duty plastic wrap, and flatten to 1/4-inch thickness using a meat mallet or rolling pin.
Sprinkle 1/2 teaspoon salt and 1/2 teaspoon black pepper evenly over chicken. Set aside.
Combine cracker crumbs, 2 cups flour, baking powder, 1 1/2 teaspoons salt, 1 teaspoon black pepper, and ground red pepper.
Whisk together 1 1/2 cups milk and eggs. Dredge chicken in cracker crumb mixture; dip in milk mixture, and dredge in cracker mixture again.
Pour oil to a depth of 1/2 inch in a 12-inch skillet (do not use a nonstick skillet). Heat to 360°. Fry chicken, in batches, 10 minutes, adding oil as needed. Turn and fry 4 to 5 more minutes or until golden brown. Remove to a wire rack in a jellyroll pan. Keep chicken warm in a 225° oven. Carefully drain hot oil, reserving cooked bits and 2 tablespoons drippings in skillet.
Whisk together remaining 1/2 cup flour, remaining 2 1/2 teaspoons salt, remaining 1 teaspoon black pepper, and remaining 6 1/2 cups milk. Pour mixture into reserved drippings in skillet; cook over medium-high heat, whisking constantly, 10 to 12 minutes or until thickened. Serve gravy with chicken.