Ah, so you claim they were a american controlled group?

While the US spend lots of effort on hunting them?

Keeping the flames high, to play firemen?

I don't think that there was a need of more flames, for that theory to be plausible. Occasionally some western weapons likely did found their ways towards IS as well, but they rather captured the bulk of it. Or do you have other sources?

Afghanistan is the obvious example, among many. Beyond that, American interventionism has fueled extremism in the region for decades. This is not a wild take, but one agreed upon by scholars.