Preheat oven to 350 degrees. Butter an 11-by-17-inch rimmed baking sheet, line with parchment paper, and butter again. Dust with cocoa powder and tap off excess. Sift cocoa, flour, sugar, baking soda, baking powder, and salt into the bowl of a mixer. Beat on low speed until just combined. Raise speed to medium, and add eggs, buttermilk, water, oil, and vanilla. Beat until smooth, about 3 minutes.
Pour batter into prepared baking pan. Bake until set and a toothpick inserted into the center comes out clean, about 18 minutes. Let cool completely in pan for 15 minutes.
Invert cooled cake onto a rack, and remove parchment paper. Then reinvert cake onto a work surface, with a long side facing you. To shape into diamonds, make parallel cuts 1 1/2 inches apart at a sharp angle to long side of cake. Then make similar cuts angled in the opposite direction.
Place diamonds on a wire rack set over a rimmed baking sheet. Pour 2 to 3 tablespoons ganache over each diamond (excess ganache can be returned to the pan, rewarmed, and then used again). Transfer cakes to a parchment-lined baking sheet, and top each with about 2 teaspoons coconut flakes. Refrigerate until set, 1 hour or up to 1 day, and serve.
Uncut, unglazed cake can be stored, wrapped in plastic, at room temperature overnight, or refrigerated up to 2 days.