In order to understand why Naruto can fly, I will give you some basis concepts of the series:
(1) The series bring the idea of elemental jutsus and the most important here is the case where the element user can become one with his element. The best example are Gaara's sand, Suigetsu's water, Hashirama's mokuton, etc. These people can become one with their element and travel in the medium of their element.
(2) The toad Pa, when he was teaching Senjutsu to naruto, said that in order to master SM, Naruto needed to become one with nature. This means once you are one, you can control, sense, and manipulate everything within Nature. When naruto was fighting Kaguya, he realized that Kaguya was one with nature as an explanation of how she was able to alter nature at will.
So, the two concept above are the same, with a slight different in both direction - that is concept (2) is the big picture while concept (1) is a subset of concept (2). Basically, Suigetsu is a master of a piece of nature aka water, Gaara mastered sand, and Hashirama wood ( water and earth).
Now, back to Naruto, he has mastered the ultimate Senjutsu by his own effort and a push from Hagoromo. Now, he is a true sage, and can sense everything in his surrounding. As consequence, Naruto is also a master of the air medium. Therefore, he can fly in the air because of his Senjutsu. In fact, Naruto can do this with every single element, and Kishi would have done it if he wanted. So, the answer of the OP is Senjutsu aka natural energy to the extreme. To those who think it is the nine bijus, they are wrong. What make Naruto go in Senjutsu of the six paths is natural energy.
