Preheat oven to 350 degrees.
Heat sugar in a small saucepan over medium heat, stirring constantly until melted and golden brown; Pour into 8-inch pan. Working quickly, swirl melted sugar around the bottom and sides of the round pan to coat.
Combine coconut milk, condensed milk, evaporated milk, eggs, and vanilla in a blender. Pour the mixture into the pan.
Prepare a water bath by placing the round cake pan in a 13×9 baking pan. Fill the outer dish with hot water to 1/2 inch depth.
Bake for 45 minutes or until a table knife inserted in the middle comes out clean. Cool on a wire rack for about 30 minutes. Then, place in the refrigerator for at least 4 hours.
To unmold, place the bottom of the pan on warm water for about 5 minutes. Run a knife around the edges of the pan. Invert a serving plate over the round pan, hold tightly and quickly turn over. Gently, shake the mold to release.
Top with coconut flakes for garnish. Refrigerate until serving time.