Preheat the oven to 350 degrees Fahrenheit.
Add the coconut flour, ground flaxseed, and baking soda to a mixing bowl, then mix well.
Add the unsweetened almond milk, almond butter, maple syrup, apple cider vinegar, vanilla extract, cinnamon, ginger, nutmeg, cloves, and salt to a second mixing bowl, then use a whisk to mix well.
Add the dry ingredients to the wet ingredients, then stir to combine.
Add the grated carrots, then stir to combine.
Transfer the batter to a 9-inch loaf pan lined with parchment paper.
Wet a spoon with cold water, then use the back of the spoon to smooth the batter into an even layer.
Bake for 50 minutes or until a toothpick inserted into the middle of the cake looks clean upon removal.
Let the cake cool to room temperature before removing from the pan and serving.