Preheat the oven to 325 degrees F (165 degrees C). Grease a 9-inch square baking dish and line with parchment paper.
Add oats to the bowl of a food processor; pulse for 10 to 15 seconds until finely chopped. Pour into a large bowl and add flour. Add liver to the food processor and process until smooth, 10 to 15 seconds. Add eggs and blend until well combined, about 10 seconds. Add oil for a little flavor and process.
Add liver mixture to oat and flour mixture and stir until well blended. Spoon into prepared baking dish.
Bake in the preheated oven until firm to the touch but not hard and crispy, 30 to 40 minutes. Remove from oven and cool on a wire rack. Cut into doggy-bite-sized pieces.
