Preheat oven to 350 degrees F (175 degrees C). Grease one 8-inch square baking dish with 1 tablespoon coconut oil.
Mix water and flaxseed meal together in a small bowl to make a "flax egg"; set aside to thicken, about 5 minutes.
Place flax egg, black beans, coconut sugar, avocado, and 2 teaspoons coconut oil in a food processor and puree until well-combined. Add cocoa powder, baking soda, and baking powder; blend until batter is smooth, 3 to 4 minutes.
Transfer batter to a large bowl and fold in chocolate chips. Pour into the baking dish and smooth the top.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 25 minutes. Cut into 16 bars and top with additional chocolate chips.