Preheat oven to 350 degrees F (175 degrees C). Place peach slices in a baking dish.
Thaw peaches in the preheating oven, about 5 minutes. Break apart and spread evenly in the baking dish. Sprinkle 1 tablespoon sugar on top.
Combine remaining 1 tablespoon coconut sugar, almond flour, coconut flakes, baking powder, and salt in a food processor; pulse about 5 times until mixed. Add butter and vanilla extract; pulse a few more times until crumbly. Pour over peaches.
Scatter slivered almonds over flour mixture. Drizzle coconut oil on top.
Bake in the preheated oven until golden brown, 22 to 25 minutes.