I know engines can be flat rated with respect to temperature. Can you explain this flat rating with altitude and speed?
Up to a point, this is possible. I've seen engines with an "altitude bump" to provide (nearly) the same static thrust at 5K (Denver or J-burg) as at SL.
But the engine has less air to work with, of course, so a full-rated takeoff at this altitude is naturally a bit harder on the hot section.