Preheat the oven to 350 degrees F (175 degrees C). Grease 3 mini muffin pans with cooking spray.
Mix water and flax meal together and set aside until gelled, about 5 minutes. Mix flour and cocoa powder in a small bowl.
Beat butter and sugar with an electric mixer in a large bowl until well combined. And 1/2 of the flax mixture and beat well. Add remaining flax mixture and vanilla extract; mix well. Blend in the flour mixture a little at a time until completely incorporated. Add zucchini with a spoon and mix well. Spoon batter into the prepared muffin pans.
Bake in the preheated oven until edges pull away from the sides of the pan, about 20 minutes. Remove from the pans and cool on wire racks.