Preheat oven to 350 degrees F. Grease a bread loaf pan with a thick layer of coconut oil and set aside.
In a medium bowl, mix flour, oats, flax, cocoa powder, baking powder, baking soda, cinnamon, and salt together and set aside.
In a large mixing bowl, mix eggs, sugar, yogurt, banana, and vanilla well using a mixer or by whisking vigorously.
Stir dry ingredients into mixing bowl with wet ingredients and stir to combine (do not over mix).
Use paper towels or a kitchen towel to squeeze excess moisture from zucchini. Add zucchini and chocolate chips to batter and stir to distribute throughout the batter.
Pour batter into pre-greased pan and put pan in center of pre-heated oven. Make sure that the second oven rack is not directly over the pan, as the bread will rise while baking.
Bake for 50 -60 minutes, until a toothpick inserted into the center comes out mostly clean and bread is set. Remove and cool on a wire rack for 10 – 15 minutes in the pan.
Run a knife around the edge of the loaf, flip, and release the loaf from the pan. Let cool completely before slicing and serving.