I think you need to make the distinction between flying by either method you mentioned and levitation.
Firebenders fly via directed propulsion; like rockets.
Airbenders fly via manipulating air currents over wings, like planes, or by propulsion (a swirling ball of air is applying force against the surrounding air).
Guru Lahima, and subsequently Zaheer, achieved levitation; flight without propulsion or manipulation of air currents. There isn't an explicit canon reason for what's going on, but the Avatar universe embodies a mish-mash of various religions. Two important contributors are Taoism and Buddhism, and for your question, you would want to take a look at Buddhism.
Not only do the Airbender monks look like their actual Buddhist counterparts (down to how Avatar Aang was chosen and how the Dalai Lama was chosen), but they share many of the same tenets. Specifically, you should look at Śūnyatā, the concept of "emptiness" or "voidness." To mangle a multi-thousand-year-old religious concept down to something more digestible: Reality sucks, and to break through the veil into heaven, you have to let go of reality in favor of meditation to achieve enlightenment.
Zaheer had a lot of time to meditate, and his last tether to reality was his interpersonal relationship with P'Li, the combustion bender. Once he presumed her dead, he achieved a stage of enlightenment that allowed him to "be empty" -- and then just levitate away.
Aang was also instructed by a Guru to "let go" of his earthly desires in order to complete his Avatar training and unclog his final chakra, but he refused to do so. Had he done so, it's possible he might have achieved a similar technique to Zaheer.
TL:DR = The religions the show heavily borrows from have a basis for achieving forms of enlightenment through inhabiting a form of emptiness through meditation. Presumably the enlightenment allows the Airbenders who achieve it to levitate at-will, and Aang might have been capable of something similar had he followed through on his Avatar training with the Guru.