Whisk together the ground flax seed and water in a small bowl until well combined. Allow mixture to sit 15 minutes, stirring occasionally, until mixture is thick and gooey, like the consistency of beaten eggs.

Preheat the oven to 350 degrees F and line a 9" x 5" loaf pan with parchment paper.

Whisk the flax eggs, mashed banana, vanilla extract, and pure maple syrup together in a mixing bowl. In a separate bowl, stir together the remaining dry ingredients. Pour the dry ingredients into the bowl with the wet ingredients and stir until combined.

Transfer the banana bread batter to the lined loaf pan and place on the center rack of the preheated oven. Bake 50 to 60 minutes, or until loaf turns golden brown and feels firm when gently poked in the center. If the loaf begins to look too brown on the top at any point, you can cover it with aluminum foil to protect the top from burning. Turn off the oven and allow loaf to sit another 8 minutes in the warm oven.

Remove loaf from the oven and allow it to cool at least 10 minutes before slicing and serving.