If, however, the wiring is to be routed inside the walls, you probably don't need metal-clad wiring. It can be more difficult to work with, driving up labour costs as time increases and, since it is physically bigger, you may not be able to run 2 circuits through the same holes in the studs. All in all, I would recommend sheathed electrical cable for most re-wiring jobs.
One place where I would use metal-clad wiring is if my walls are quite thin and I don't have 1-1/4" of room between the nailing surface and the wire. You might get this with basement walls that have been strapped or walls with pocket doors. In this case, you would have to install a metal plate over each stud or strap to protect the wiring, but the metal-clad wiring wouldn't need that. You could just drill your holes and pull it through.
I, too, do not know what "flex" means (not a standardized term of art), but suspect that it refers to the non-metallic "sheathed electrical cable" wire to which the others referred. What he meant probably depends on wiring code and practice in your area. Some places prohibit NM cable, some prohibit armored cable, but they are all reasonably safe products.
Regardless of what he means, I feel confident that he will be installing safe wire. Most unsafe electrical wiring products have been weeded out of the common market by now, so much so that it is even tough to find stuff for outdated wiring products that are "grandfathered" into electrical codes (like aluminum wiring). It is all pretty standardized throughout the country, whether they typically use NM cable, flex-metal cable, or plastic or metal conduit. Of course, we might find out in a few years that copper electrical wire is the REAL cause of AIDS or something else unpredictably horrible (for instance, they thought aluminum wire was safe for three or four years before they discovered the hazards, and that rubber was a good insulator until it deteriorated industry-wide after 20 or so years), but if that is the case, we're all in it together.