Going by what I remember from the movie, they never said what it was that gave him propulsion, or what exactly came out of his hands when he was shooting things with them. The important part of his technology seemed to be the immensely energy dense power source located on his chest.
I suppose a different question could be asked, if you could have a lightweight, nearly infinite power source how would you use it to fly? The suit was too small to have any kind of propellant, and this makes the form of propulsion interesting if the only real physical rules being violated here are those dealing with the power source and the unobtanium the suit was made out of.
I suppose, if I had an infinite power source, I could figure out some way to intensely heat a region of air and eject it, maybe stripping it into a plasma so that I could use E&M fields to grab the plasma. But I don't see such a thing being possible in real life because of the materials and energy required, along with the sheer inefficiency of the thing.