Put 2 cups of the oats in a blender or food processor and grind into a fine powder. Combine with the remaining ½ cup oats, potato starch, rice flour, flax seed meal and salt in a large mixing bowl. Mix in the egg and olive oil. Mix the dry milk powder with the water and combine with the rest of the ingredients.
Grate the sweet potato using the large holes of a box grater. Stir into the mixture. The dough should be firm, smooth and workable. If not, add more rice flour. Cover the bowl with a towel and let set for 20 minutes to let the moisture distribute.
Preheat oven to 250 degrees. Line 2 baking sheets with parchment paper or Silpat mats.
Flour a work surface with rice flour and roll the dough out to either ¼-inch or ½-inch thick (depending on the size of your dog). Cut the biscuits out with a dog bone shaped (or any shape you like) cookie cutter, pressing firmly to cut through the sweet potato. Transfer the biscuits to the prepared pans.
Bake for 1½ to 2 hours or until the biscuits are dry and firm. Let cool completely.
Store the Gluten-free Dog Biscuits in a food storage bag or airtight container.