Preheat oven to 350 degrees F (175 degrees C). Spray muffin cups with cooking spray or line with paper liners.
Beat sugar, butter, flax seed, vanilla, and eggs together in a bowl with an electric mixer until smooth and creamy.
Sift flour, salt, and baking soda together in a separate bowl. Mix creamed sugar mixture, 1/2 cup at a time, into the flour mixture until fully incorporated and batter is stiff. Beat bananas into batter with an electric mixer on low. Fold chocolate chips and walnuts into batter; spoon into the prepared muffin cups, filling each cup 3/4 full.
Bake in the preheated oven until a toothpick inserted in the center of a muffin comes out clean, about 25 minutes. Cool in the tins for 10 minutes before removing to cool completely on a wire rack.