Poke the sweet potatoes all over with a fork and wrap in foil. Bake until the potatoes offer no resistance when pierced with a paring knife, about 1 hour. Unwrap and let cool completely.
Scoop the insides of the potatoes into a bowl and mash with the back of a fork (you will need 1 3/4 cups of the puree). Stir the chicken bouillon into 1 cup of hot water and add to the potatoes; whisk until smooth. Stir in the oat flour, rolled oats and baking soda until a dough forms. Wrap in plastic wrap and refrigerate for 2 hours or overnight.
Adjust the oven temperature to 350 degrees F. Line 2 baking sheets with parchment paper.
Lightly flour a clean work surface with oat flour. Divide the dough in half and roll out 1/8-inch thick. Use a 3-inch dog-bone-shaped cookie cutter to cut out the treats. Gather the scraps and re-roll the dough as many times as necessary. Lay the treats on the prepared baking sheets; they can be very close together.
Bake until deep golden brown and crisp, 25 to 30 minutes. Remove from the oven and let cool completely before feeding to your dog. Store in an airtight container at room temperature for 4 to 5 days.