We most certainly are not going to "get" Iraq's oil. At best we will help arrange for Iraq's oil to reach the market in a stable way. To "get" it we will still have to buy it.
Iran? Russia? China?
Iran and Russia have plenty of oil.
I believe China already has deals to buy Iraqi oil.
Oil is a commodity and will be sold on the world market. Everyone will "get" Iraq's oil. That is, if Iraq can get their act together and bring its full potential to market.
What will not happen (what you seem to be wishing for) is that the U.S. will not take possession of Iraq's oil fields fullstop, and sell it ourselves, keeping the entire net. There are two reasons for this. 1. It would be hard to protect that possession even once seized. We're having a difficult enough time as it is just remaining in-country on secure bases as it is. 2. That would actually just be plain, baldfaced imperialism.
Not that there's anything wrong with that.