Preheat oven to 165 degrees C. Grease and flour two 23 x 13cm bread tins.
Mix together the flour, linseeds, salt, bicarb soda, cinnamon, baking powder and arrowroot in a bowl until evenly blended; set aside.
Whisk together the apple sauce, brown sugar, vegetable oil and vanilla essence in a bowl until smooth. Fold in the flour mixture and grated zucchini until moistened. Divide the batter between the prepared bread tins.
Bake in the preheated oven until a toothpick inserted into the centre comes out clean; about 70 minutes. Cool in the tins for 10 minutes before removing to cool completely on a wire rack.