Sprinkle 1/2 cup sugar in a 9-inch round cakepan. Cook over medium-high heat, shaking pan occasionally using oven mitts, until sugar melts and turns a light golden brown; set aside. (Mixture may crack slightly as it cools.)
Heat milk and remaining 1/2 cup sugar in a heavy saucepan, stirring constantly, until hot and frothy.
Beat eggs, egg whites, and next 3 ingredients at medium speed with an electric mixer until blended; gradually add hot milk mixture, beating at low speed. Pour mixture over caramelized sugar, and place cakepan in a roasting pan. Pour hot water into roasting pan to a depth of 1 inch.
Bake at 350° for 1 hour or until a knife inserted in center of flan comes out clean.
Remove pan from water; cool on a wire rack. Cover and chill.
Bake coconut in a shallow pan at 350°, stirring occasionally, 5 to 6 minutes or until toasted. Cool.
Loosen edges of flan with a spatula, and invert onto a serving plate. Sprinkle with coconut.