Preheat the oven 350 degrees F. and line a large baking sheet with parchment paper.
Make the flax egg in a small bowl by combining 2 tablespoons of ground flax meal with 4 tablespoons of water. Allow the flax egg to sit for a few minutes to thicken while you begin making the treats.
In a medium bowl, stir together the coconut flour, peanut butter, coconut oil, sweet potato puree, and the flax egg. Stir until it comes together in a dough and then mix by hand until it all comes together. Place on a large piece of parchment paper and cover with another piece of parchment paper and roll out ¼-inch thick using a rolling pin.
Use cookie cutters to make the treats and place them on the prepared baking sheet. Place in the oven and bake for 12 to 15 minutes, until they turn golden brown. Place on a cooling rack to allow the sweet potato dog treats to cool completely prior to serving. Store in an airtight container.