Preheat the oven to 350°F and grease two 4-inch cake pans with coconut oil. Place a circle of parchment paper on the bottom of each pan.
In a small bowl, whisk the flaxseed with hot water. Set aside and allow it to set up slightly. This will act as an egg.
In a large bowl, sift the flour, baking powder, baking soda, and salt.
Add the mashed banana, strawberries, and applesauce to a blender or food processor. Blend until well combined into a puree.
Transfer the fruit mixture into a medium bowl and add the milk, flax "egg", and vanilla.
Pour the wet ingredients into the dry and mix until just combined.
Evenly distribute the batter between the two cake pans and bake for about 20 minutes. Check with a toothpick for doneness. It should come out clean when inserted into the center of each cake.
When the cakes are done, let them cool for 10 minutes before releasing from the pans. Then allow them to cool completely.
When they are totally cool, tightly wrap each one in plastic wrap, followed by aluminum foil. Freeze for at least 2-4 hours and up to a few weeks if making in advance.