Prior to the Parliamentary vote, I expect it would have been difficult for the RAF to allow the use of Akrotiri for other nations to launch operations against Syria.
Now the vote has been taken and the RAF will have 16x FJ there, I wonder if other nations may request/be invited to use Akrotiri. It seems ideally situated, and more easily defended than bases in neighboring countries to Syria.
It's many years since I went to AKT, but from what I recall, it's on a bit of a peninsula and the actual airfield is miles past the gate.