Much of the Iraqi oil lies in the North and the South - so the Kurds would be OK - apart from they are left with the daunting problem of exporting oil either N through Turkey - who are kind of hostile to the overall concept of Kurdistan - or South through what is currently Iraq.  I'm not sure that the Sunnis actaully get left with anything - which may be one of their current concerns.
Turkey worries that an independent Kurdish state on their border would attempt to incite separatist Kurds inside Turkey. That's a bit of a political hot potato there.
I don't think Iran would like to see an Independent Kurdistan either.

http://en.wikipedia.org/wiki/Kurdish_people#Kurds_in_Iran

GreyZone,

And the Iranians with their sizeable minority. But the Kurds did secure some oil for themselves.