Preheat oven to 350°F. Line an 8x8 baking dish with parchment paper. Allow the parchment paper to hang over two opposites sides of the dish to use as "handles" later when lifting out the cake. See photos, if necessary.
Whisk flour, flaxmeal, baking powder, baking soda, and salt in a small mixing bowl.
In a larger mixing bowl, whisk together the smashed bananas, coconut sugar, apple cider vinegar, vanilla, and non-dairy milk.
Whisk the dry ingredients into the wet until combined. Don't over mix. Make sure there is no white flour visible, but a few lumps are fine and expected because of the bananas.
Stir in the chocolate chips.
Pour the batter into the prepared baking dish.
Bake 30 to 35 minutes until a toothpick inserted in the center comes out clean.
Let cool in the pan for 10 to 15 minutes before lifting out and continuing to cool on a cooling rack.
Cut into squares and enjoy.