The only possibility I can see is if you get a very different Anglo-Iraqi War. If you could get Syria and Iraq both to rise up in 1940-41 against the British and Free French regimes, and get the Kurds to side with the allies than you might have a chance. After putting down the nationalist/pro-axis rebels in Syria and Iraq the Free French and British governments decide to carve out an independent Kurdish state from the Kurdish regions of Iraq and Syria. You might also be able to get Iranian Kurdistan added as well because of the Anglo-Soviet occupation of Persia.
However this requires a PoD sometime in the early 30s at the latest. You would also need to get the local regimes of both Syria and Iraq to join the rebels. In Syria this isn't as much of a problem because Syria revolted against the French several times during its Mandatory period. However in Iraq this would be more difficult. In Iraq the rebels of OTL Anglo-Iraqi War expelled the British backed Hashemite dynasty. In that circumstance I don't think the British carve off a piece of Iraq for the Kurds. You would need this rebellion to be backed, if not started, by the Monarchy.
The difficulty would be in getting the Kurds to side with the British and French. In Iraq the Kurds rose up against the Hashemite monarchy(backed by the British) several times. In the wake of the Ottoman collapse the Kurds had proclaimed their own kingdom that lasted from 1922-1924. During the Anglo-Iraqi War the Kurds took control of their region of Iraq until 1945 when the British could spare forces and put down their insurgency.
So if you want an independent Kurdistan than you want an earlier PoD. My suggestion is to have the British support the Kingdom of Kurdistan after the collapse of the Ottoman Empire and simply establish it as a British Mandate.