Gather the ingredients. Preheat the oven to 325 degrees F (165 degrees C). Grease and flour two 9x5-inch loaf pans.

Whisk flour, flax seeds, cinnamon, salt, baking soda, baking powder, and arrowroot together in a bowl until evenly blended; set aside.

Whisk applesauce, white sugar, brown sugar, vegetable oil, and vanilla extract in a separate bowl until smooth. Fold in flour mixture and shredded zucchini until moistened.

Divide 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 briefly in the pans before removing to cool completely on a wire rack.