Don't know a whole lot about the situation in the Gulf region, specifically Iraqi/Kuwaiti co-ordination, but I do know this - during ATC training we were taught that a TCAS RA would not advise/instruct a crew to initiate lateral manoeuvers for traffic advise, that it's extent was limited to the vertical plain. Maybe I'm wrong, or maybe the technology has progressed a bit since then?!
Also, as the mil controller had handed off the C130 to Kuwaiti control, he may well not have seen it on his radar when the incident occurred. As has already been mentioned above, mil crews are in the habit of intermittently using their transponders when operating when in a hostile environment (which I'm in no doubt that some or many of them view Iraq as such). There is also the possibility that as co-ordination and the radar hand-off had already been effected between the military and Kuwaiti controllers, the filters on the mil radar may have been set to exclude detailed info on this fllight from the display!
I could be way off the mark with these comments, but I think there could be any number of explanations. One possibility I would hate to contemplate of course would be any complacency or lack of professionalism on the part of ATC, either military or civilian, although it cannot be ruled out. Just have to wait and see what results from the investigation (if anything!!)
Either way, I take my hat off to you Waldo. IMHO, your teamwork, sound decision-making, and quick reaction to a potentially catastrophic situation undoubtedly saved the day.
Definitely strengthens the arguments for alertness and good situational awareness.
Let's just hope the stuation isn't white-washed, so that some other poor sod doesn't find himself in a similar situation in the future, that may not be so easy to get out of!!