Combine 1 1/4 cups sugar and oil in a large bowl, beating well at medium speed of an electric mixer. Add eggs, 1 at a time, beating well after each addition.
Combine flour, baking soda, and salt; add flour mixture to sugar mixture alternately with buttermilk, beginning and ending with flour mixture. Mix after each addition. Stir in vanilla.
Combine 1 cup batter, coconut, and 1 teaspoon coconut flavoring in a small bowl; stir well. Set aside. Add cocoa to remaining batter in large bowl; stir well. Reserve 1 cup chocolate batter and set aside. Pour remaining chocolate batter into 12-cup Bundt pan coated with cooking spray. Spoon coconut batter over center of batter to form a ring making sure not to touch sides of pan. Top with reserved chocolate batter, spreading evenly to cover.
Bake at 350° for 40 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes; remove from pan. Cool on a wire rack. Combine remaining 1/2 teaspoon coconut flavoring, powdered sugar, and skim milk; stir well. Drizzle over cake.