Even if the Gulf states wanted to help, they might find it very difficult to do so, bogged down as they are in Yemen. Maybe an odd air-strike and perhaps some financial assistance.The Turks have good reason to be worried. The priority for Syria and Russia will not only be to push back IS from areas they occupy but also to cut the land routes from Turkey.
It will safe the assume that the Iraqis are under pressure not to accept any large scale help from Russia, for which the right thing would be for the Sunni Arab Gulf states to provide more assistance to Iraq; unlikely to happen.
In the case of the latter, Iraq might end up buying more Russian gear on top of what it has already purchased.
I am somewhat surprised with the short-sightedness of Erdogan's politics. He huffs and puffs not realising that it may leave Turkey even more alienated from its neighbours.