Place each chicken breast half on waxed paper; flatten to 1/4- inch thickness using a meat mallet or rolling pin.
Combine flour, salt, and pepper in a plastic or paper bag; shake to mix. Place 2 or 3 pieces of chicken in bag; shake well. Repeat procedure with remaining chicken.
Heat oil in a large skillet. Add chicken; sauté over medium heat 7 minutes on each side or until golden brown. Drain; reserve oil in skillet. Marinate chicken in Red Gravy Sauce 10 minutes.
Sauté eggplant in reserved oil until golden brown on both sides; drain and set aside.
Cook vermicelli according to package directions; drain. Spoon into a lightly greased 13- x 9- x 2-inch baking dish. Sprinkle mushrooms evenly over vermicelli. Place chicken breasts over mushrooms, and cover with sauce. Top with eggplant and cheese slices. Bake at 375° for 15 minutes or until cheese melts and sauce is bubbly.