The video says itself this is not the power of flying or levitation. The power of flying is
described in the Yogasutras by Patanjali, which is one the
siddhis or powers that can
be developed in Yoga. In order do this you must reach a stage known as Samyama, or perfect
concentration, which is a prerequiste for activating any power. When Samyama is applied on
various objects the power is activated.
3.4 The three processes of dharana, dhyana, and samadhi, when taken together on the same object, place or point is called samyama.
(trayam ekatra samyama)
Dharana: Concentration is the process of holding or fixing the attention of mind onto one object or place. (3.1)
Dhyana: Meditation is sustained concentration, whereby the attention continues to hold or repeat the same object or place. (3.2)
Samadhi: Samadhi is the deep absorption, wherein only the essence of that object, place, or point shines forth in the mind, as if the mind were devoid even of its own form. (3.3)
3.5 Through the mastery of that three-part process of samyama, the light of knowledge, transcendental insight, or higher consciousness (prajna) dawns, illumines, flashes, or is visible.
(tad jayat prajna lokah)
The various powers and how they are activated:
Seeing into the past and future:
3.16 By samyama on the three-fold changes in form, time, and characteristics, there comes knowledge of the past and future.
(parinimah traya samyama atita anagata jnana)
Universal language translation:
3.17 The name associated with an object, the object itself implied by that name, and the conceptual existence of the object, all three usually interpenetrate or commingle with one another. By samyama on the distinction between these three, the meaning of the sounds made by all beings becomes available.
(shabda artha pratyaya itaretara adhyasat samkara tat pravibhaga samyama sarva bhuta ruta jnana)
Knowledge of past lives:
3.18 Through the direct perception of the latent impressions (samskaras) comes the knowledge of previous incarnations.
(samskara saksat karanat purva jati jnanam)
Seeing into anothers mind:
3.19 By samyama on the notions or presented ideas comes knowledge of another's mind.
(pratyayasya para chitta jnana)
Invisibility:
3.21 When samyama is done on the form of one's own physical body, the illumination or visual characteristic of the body is suspended, and is thus invisible to other people.
(kaya rupa samyama tat grahya shakti tat stambhe chaksuh prakasha asamprayoga antardhanam)
Eradicating hunger and thirst:
3.31 By samyama on the pit of the throat, hunger and thirst leave.
(kantha kupe ksut pipasa nivrittih)
Entering anothers body:
3.39 By loosening or letting go of the causes of bondage and attachment, and by following the knowledge of how to go forth into the passages of the mind, there comes the ability to enter into another body.
(bandha karana shaithilyat prachara samvedanat cha chittasya para sharira aveshah)
Levitation, flying, walking on water:
3.40 By the mastery over udana, the upward flowing prana vayu, there is a cessation of contact with mud, water, thorns, and other such objects, and there ensues the rising or levitation of the body.
(udana jayat jala panka kantaka adisu asangah utkrantih cha)
Increasing and decreasing ones size, and controlling the elements:
3.45 By samyama on the five forms of the elements (bhutas), which are gross form, essence, subtleness, interconnectedness, and its purpose, then mastery over those bhutas is attained.
(sthula svarupa suksma anvaya arthavattva samyamad bhuta-jayah)
3.46 Through that mastery over the elements, comes the abilities of making the body atomically small, perfect, and indestructible in its characteristics or components, as well as bringing other such powers.
(tatah anima adi pradurbhavah kaya sampad tad dharma anabhighata cha)
Teleportation:
3.43 By Samyama on the relationship between the body and space (akasha) and by concentrating on the lightness of cotton, passage through space can be attained.
http://www.swamij.com/yoga-sutras.htm