The following are the ninjas in the Naruto series who can fly continuously using a jutsu for propulsion (without using a summoned animal) by order of appearance.
Hoshigakure shinobi are able to use the Mysterious Peacock Method: Wings technique to achieve flight by creating feathers made of chakra to form wings. Extensive flight has not been seen, but the wings are able to hold a grown human being for short flights. Akahoshi, Natsuhi, and Sumaru all displayed the ability to use this technique. Sumuru was able to use his wings as an offensive attack as well.
Gaara is able to levitate himself anf fly using his sand as a carrier. His control over sand allows him to use his sand to levitate and fly other people or objects. It is persumable that all the previous Jinchuriki of Shukaku would be able to use this technique to some extent, as Gaara's control of sand comes from being Shukaku's host.
Deidara's Kekkei Genkai the Explosion Release allows Deidara to create objects out of clay that detonate at his will. He is shown in several instances flying on a giant clay bird that he created out of clay. The bird is created by Deidara's clay in a small form. As he pours chakra into it, the bird grows to a large size. Deidara is able to control the bird at will and can dodge several attacks while riding on it. In addition to being able to give the user access flight, the clay bird will also explode.Super Beast Imitating Drawing technique to create large flying birds. These birds are made out of special ninja ink on Sai's Super Beast Scroll. Once drawn, the birds grow to their full size, similar to Deidara's clay birds. The sizes of the birds vary, but they can be large and sturdy enough to carry two people. They are mostly created for long distance transportation, though Sai has attached Paper bombs to his birds. When dispelled, the birds will turn to ink. transform herself into paper. Once transformed to paper, Konan can spread out all the multiple sheets of paper and turn them into butterflies or airplanes for quick travel. When keeping her ultimate form, Konan can still fly, but she often summons paper wings for addition power.
Ohnoki and Mū can fly using their Flight Technique and can also enable others to fly by touching them. Flight is easy and free. The user can easily fly around and their movement is unrestriced and free. This technique may be related to the Earth Release: Super Light-Weight Rock Technique and the Dust Release. Ohnoki enabled Kurotsuchi and Akatsuchi to fly for a long period of time.