the bit 'controlled' by the government seems about the least stable bit of Iraq - army falling apart, two people calling themselves PM...
the Turks look like the don't want to get involved in this one - unless the USN is flying 2000km+ missions for the good of its health - best bet is FOBing in the Kurdish state/region...
can't see how it will come off without a UK ground security force, and it'll take more than two C-130's in Cyprus to keep the Chinooks both flying and in stuff to deliver.