The BJCP guidelines classify oatmeal stout as a variant of sweet stouts as opposed to dry stouts, but mention that the sweetness can vary quite a bit. They usually fall somewhere in between a dry and sweet stout though.
I'd include at least a bit of crystal malt, to keep some sweetness in there. My oatmeal stout uses:
13% flaked oats (toasted)
10% roast barley
10% crystal 80L
5% chocolate malt