I don't think the current developments have anything to do with the Kurds.

Sure, the Kurds would ideally like their own state, but are unlikely to rock the boat, as they are likely to get a high degree of autonomy in the new Iraq.

Iran is increasing its troop strength on the southern border, which is as far away the Kurds as you could get!
Which, incidentally would bring them into conflict with UK forces, not the US.

This comes down to the fact that Iran has most of its support in the south - because the Muslim creed they support there is the same as in Iran - i.e. Shiite, not Sunni like in the north.
And these two creeds hate each other, in much the same way that Protestants and Catholics have killed each other in Northern Ireland.

Iran would love to annex part of southern Iraq, as for example Basra has huge strategic importance - did anyone mention oil ??