Trim excess fat from steak. Pound steak to 1/4-inch thickness; cut into 6 serving-size pieces.
Combine 1/3 cup flour and 1/4 teaspoon pepper. Dredge steak in flour mixture. Lightly pound floured steak. Heat oil in a large skillet over medium heat. Add steak; cover and cook 10 minutes. Uncover and cook an additional 5 minutes, turning to brown evenly. Remove steak, reserving pan drippings in skillet. Drain steak. Sprinkle with salt to taste.
Add 2 tablespoons flour to drippings, stirring until smooth. Cook over low heat 1 minute, stirring constantly. Gradually add milk, coffee, and water; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in 1/4 teaspoon salt and 1/8 teaspoon pepper. Serve gravy with steak.