Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Blend black beans in a blender until smooth. Add bananas and vanilla extract; blend until smooth. Gradually add dates, a few at a time, and blend until evenly incorporated.

Whisk oat flour, cocoa powder, flax seed, baking powder, and baking soda together in a bowl. Beat bean mixture into flour mixture on low to medium speed until batter is well blended; fold in walnuts. Spoon batter into prepared baking dish.

Bake in the preheated oven until edges of brownies begin to pull away from sides of dish, about 50 minutes.