Not getting into an argument over KC135 vs 707 since I have flown both, but the FAA issued me a 707 type rating based on my flying the 135. The systems are very different, and the 135 is both shorter and narrower than the 707-320Bs that I flew, but they fly pretty much the same. The biggest difference is in the landing. The 707 has slats that the 135 does not and touches down at a much steeper deck angle. My first few landings in the 707 were interesting to say the least. At least I was flying freight and Mr. Box doesn't complain about firm touchdowns.
You should have paid more attention then as the KC-135 does have leading edge devices. I won't get into the argument of whether they should be referred to as slats or flaps, but the manual calls them flaps. The big difference is the length of the leading edge devices. The KC-135 only has a short span between the engines, on the 707 they are much longer.
S-D