Preheat the oven to 350°F.Line a loaf pan with parchment paper or spray with cooking spray.
In a medium bowl, combine the coconut milk and vinegar. Whisk and set aside.
In a large bowl or stand mixer, combine buckwheat flour, cinnamon, baking powder, baking soda, and salt. Stir until blended.
To the bowl with the coconut milk and vinegar, mash in the banana, and add the vanilla extract. Whisk until creamy. You can also blend these ingredients together in a blender.
Pour the wet ingredients into the bowl with the flour mixture and beat until a batter is formed. Fold in the walnuts. Transfer the batter to the loaf pan.
Bake for 40 minutes. Remove the pan from the oven to turn, covering with a piece of foil to prevent burning on the top. Bake for another 10-15 minutes until toothpick comes out clean or internal temperature is at least 180 degrees. Allow the bread to completely cool in the pan, about 1-2 hours.