When he made that giant Rasenshuriken on top of Gamakichi, my first thought was that he had created a Toad-copter and was flying. However, I now know that is not the case.
Imo, Naruto will eventually be able to fly. So far he's fought Obito, who could fly as Juubi Jin...I think Naruto may gain this power when he channels his Bijuu power. Likewise, Sasuke will be able to fly using his gravity-manipulating Rinnegan (and create a winged Susano'o).
Finally, it's unclear whether the giant chakra-bird formation used by the Shinobi Alliance was actually flying when it cut through the Juubi limbs and reached Madara/Obito... If so, Naruto may be able to use his chakra to fly.