Preheat the oven to 170°C. Grease and line a medium loaf tin.
Mix the ground flaxseeds and water to create the flax-egg and rest for 5 minutes until it becomes gooey.
Mix the vinegar and milk, then rest for about 5 minutes until it's curdled.
Mash the bananas with a fork. Add the cinnamon and oat, combine well. Grate one apple and add to banana mixture together with the sugar and oil. Add the curdled milk and flax egg and gently combine, then fold in the flour and baking powder.
Cut the other apple into 1 cm cubes.
Fold the apple and walnut pieces into the batter.
Tip the mixture into the prepared loaf pan, spreading it out evenly.
Bake for 50-60 minutes or until a toothpick inserted into centre comes out clean.
Let it cool in the tin for 5 minutes, then transfer it to a wire-rack.
When the cake has completely cooled, slice and serve.