Preheat oven to 350°F. Grease a baking sheet or line it with a silicone mat or parchment paper.
Make a flax egg by combining flaxseed and water in a small bowl. Allow the mixture to sit for 5 minutes.
Place the flax egg, applesauce, and peanut butter in a medium bowl.
Use a hand mixer or a large spoon to combine the wet ingredients.
Add the rice flour and combine well to form a dough.
Turn the dough out onto a smooth surface.
Using your hands, squeeze and combine the ingredients until you have a flat, smooth dough. Flatten the dough evenly with your hands or a rolling pin to about ¼ to ½-inch thickness.
Using a cookie cutter, cut out the dog treats and place them on the prepared baking sheet.
Bake for 12 to 16 minutes.
Transfer the baked treats to a wire rack to cool to room temperature.