Forgive me if I make the wrong assumption here, but I've heard the term "axle flip" many times. This term is somewhat misleading, and the proper way to describe it is as a Spring Over Axle conversion, or SOA. I had a guy actually explain the process of flipping the axles over.....of course this is far from what happens. The axles atay in the same relationship to the Jeep. You will be removing the springs from their original perches which are under the axle, and placing them on top of the axles by welding new spring perches up there. This gives you a lift equivalent to the diameter of the axle, the height of the perch and the thickness of the spring pack. Like currupt said, about 5-6". If you already knew that I'm sorry, I just didn't want you planning on an impossibility.
A SOA is often difficult to correctly set up. It's important that you said he wasn't really interested in max flex.....because that is the point of most SOA setups, and you may actually wind up spending more time and money than you would just buying a spring lift and staying SUA unless you can fabricate everything yourself.