Preheat oven to 325 degrees F (165 degrees C). Grease and flour two 9×5 inch loaf pans. Whisk together the flour, flax seeds, salt, baking soda, cinnamon, baking powder, and arrowroot in a bowl until evenly blended; set aside.
Whisk together the applesauce, white sugar, brown sugar, vegetable oil, and vanilla extract in a bowl until smooth. Fold in the flour mixture and shredded zucchini until moistened. Divide the batter between the prepared loaf pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 70 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
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