You have a choice, and you'll need to let your palate guide you. You need to taste it and compare to the BJCP guidelines for the styles.
If you enter it as an American Brown Ale, the judges won't know about the oatmeal - if the oatmeal pushes the taste outside the Brown Ale boundaries, the judges may mark it down.
If you enter it as a Specialty Beer, you'll need to indicate the base style (American Brown Ale) and the special ingredient (toasted oatmeal). The judges will evaluate both - is it a good representation of the base style and is the special ingredient apparent, appealing, etc. If the oatmeal doesn't stand out, it may get marked down.