Oats (ground or oatmeal) may seem like a great treat for your dog, but this type of food should be given sparingly. The reason for this is simple- oat is a filler, more or less, and while fibrous and containing protein, does not contain enough nutrients for a dog to use as a stand-alone product.
That being said, it is an excellent form of fiber and can prove to be a diuretic as well. So, this means if you have a dog who is prone to bed-wetting, oats may not be a favored form of treat. If your dog is sensitive to wheat and rice, however, oats, are OK.
Listen to your dog's response to being fed oats (such as bed-wetting, gas, vomiting, or loose stools) to see if oats are the right type of substance to give your dog. Replacements for oat include flaxseed, sweet potato, or even barley if your dog has a sensitive tummy. Talk to your vet first before moving forward.