Preheat oven to 325 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Mix ground flax seeds with 1/3 cup water in a bowl; let sit until thickened, about 10 minutes.
Sift flour, cocoa powder, baking powder, and salt into a bowl.
Melt chocolate chips and coconut oil in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each melting, 1 to 2 minutes. Let cool.
Beat flax seed mixture, remaining 1/3 cup water, sugar, and vanilla extract in a bowl with an electric mixer until creamy, about 3 minutes. Add flour mixture and melted chocolate; mix until well combined. Shape dough into 1-inch balls. Roll in confectioner's sugar and place on the prepared baking sheets.
Bake in the preheated oven until firm to the touch, 11 to 13 minutes.