Preheat oven to 375 degrees F (190 degrees C). Grease 2 loaf pans.
Whisk white sugar, oil, eggs, brown sugar, and vanilla extract together in a large bowl. Fold in grated zucchini. Add 1 1/2 cup all-purpose flour, whole wheat flour, flaxseed meal, cocoa, cinnamon, baking powder, baking soda, salt, and cardamom; mix until batter is combined.
Combine blueberries and 2 tablespoons all-purpose flour in a small bowl; toss to combine.
Fold blueberry mixture gently into the batter. Pour batter into loaf pans, filling each one 2/3 full.
Bake in the preheated oven until a toothpick inserted into the center of each loaf comes out clean, 45 minutes to 1 hour.
