There are about 41 billion barrels of oil under Iraq. If you gave everything north of Tikrit to the Kurds, they would get about 1.7 billion barrels of oil in the deal. Almost all the oil in Iraq is in the southeast, near Kuwait. Even if you gave them the oil fields southeast of Tikrit, that would only bump them up to about 2 billion barrels.

2 billion out of 41 billion? The oil is not a big issue. Maybe the pipelines from Mosul to the Mediterranean Sea ports are, but I don't think the ones through Syria are operating. The Jordanian-Israeli pipeline might be (or at least could be if you chased ISIL away from it in Iraq).