ATL84IA160

Kansas city ARTCC (zkc) had cleared ozark flt 709 (a DC-9, N923L) to cruise at FL270. While proceeding ese near the edgeof the zkc area, the DC-9 converged on zorro 11 (a flt of 3 F-4'S). The F-4'S had been cleared by indianaplolis ARTCC (zid) to proceed westbound at FL260 to rendesvous with a KC-135 tanker (shake 81) to refuel on aerial refueling route AR110W. The beginning of AR110W was in the zid area; from there it continued westbound into the zkc area. The tanker wasorbiting under control of zkc & was cleared to maintain block alt FL260 to FL290. Zid cleared the F-4'S to the tanker freq without handing them off to zkc & without obtaining approval from either zkc or the tanker. After establishing radio contact, the tanker crew incorrectly cleared the F-4'S to climb to FL270. When the zkc controller realized the F-4'S & DC-9 were converging, he told the DC-9 crew to immediately turn left. The DC-9 crew saw the F-4'S & took evasiveaction. Zid had not properly coordinated the F-4S' position & none of the plts were informed of conflicting traffic.