Preheat oven, prep pan, and mix flaxseed and water: Preheat oven to 350°F. Oil and flour a 9-by-5-inch loaf pan. Sprinkle flaxseed over ⅓ cup water. Let stand until slightly thickened, about 5 minutes. Stir to combine.
Mix dry ingredients: In a large bowl, whisk together flour, sugar, baking soda, and salt.
Add remaining ingredients: Stir in oil, almond milk, flaxseed mixture, bananas, and vanilla.
Bake and cool: Bake until a toothpick inserted in center comes out clean, 60 to 65 minutes. Let bread cool in pan 15 minutes. Remove bread from pan and let cool completely on a wire rack.
