Prepare white cake mix as directed on package directions. Beat coconut extract into the cake batter and pour batter into a greased and floured 9x13-inch baking dish. Bake cake according to package directions. Remove cake from oven. While still hot out of the oven, use a drinking straw to poke holes about an inch apart on the cake surface.
Mix cream of coconut and sweetened condensed milk together. Slowly pour the creamy coconut mixture all over the top of the hot cake and let it soak into the cake.
Let the cake cool completely, then frost to top with the whipped topping, and then sprinkle the flaked coconut over the whipped topping.