Preheat oven to 350°. Oil a 9- by 9-in. baking pan and line bottom with a sheet of parchment paper large enough to come up 2 opposite ends of pan and hang over sides. Put cherries in a small bowl and pour in liqueur. Let soak 30 minutes. Meanwhile, toast coconut on a rimmed baking sheet until golden, 3 to 5 minutes.
Meanwhile, in a microwave-safe bowl, melt 3/4 cup chocolate chips with the coconut oil, heating in 20-second bursts and then stirring, until chocolate is 3/4 melted. Stir until melted, then cool slightly.
Whisk flour, cocoa powder, and salt together in a medium bowl. Add sugar, eggs, and vanilla to melted chocolate and whisk to mix. Whisk in flour mixture. Drain cherries (save liqueur for cocktails). Stir cherries and remaining 3/4 cup chocolate chips into batter.
Pour batter into prepared pan. Bake until a toothpick inserted in center comes out clean, 25 to 30 minutes. Let brownies cool (or chill), then lift out using parchment paper and cut into 1 1/2-in. squares.
Arrange brownies on a serving tray and top with coconut flakes.
*Virgin coconut oil is cold-pressed, isn't hydrogenated, and has a clean, sweet taste. Find it, along with coconut flakes, at well-stocked grocery stores.
Make ahead: 3 days, chilled airtight.