Place chicken breasts between 2 sheets of heavy-duty plastic wrap, and flatten to a ¼-inch thickness, using the flat side of a meat mallet or rolling pin.
Sprinkle ½ teaspoon salt and ½ teaspoon black pepper evenly over chicken.
Set aside.
Combine cracker crumbs, 2 cups flour, baking powder, 1½ teaspoons salt, 1 teaspoon black pepper, and ground red pepper.
Whisk together 1½ 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 ½ 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 jelly-roll pan.
Keep chicken warm in a 225° oven.
Carefully drain hot oil, reserving cooked bits and 2 tablespoons drippings in skillet.
Whisk together remaining ½ cup flour, 2½ teaspoons salt, remaining 1 teaspoon black pepper, and 6½ cups milk.
Pour mixture into reserved drippings in skillet; cook over medium-high heat, whisking constantly, 10 to 12 minutes or until thickened.