Parkeur

Because they do flips it's called tricking, not Yamakasi.

In Parkour, flips are only included if they increase the efficiency of a movement, but that's a somewhat rare issue, because using something like a dive-roll is a more fluid and efficient action.

Free-running and Yamakasi encourage aesthetic movements in addition to fluid movement, even when it isn't necessary or may be less efficient.

Yamakasi is derived from Parkour practitioners who changed the focus of their Parkour style from efficiency to include an emphasis on aesthetic and style.

While Parkour has some vault movements which are technically complicated and skillful, these movements are inefficient and often unnecessary and thus, are looked down upon as not truly representing 'Parkour'. This isn't to mean that some vaults aren't greatly functional, its just to express that aesthetic moves exist but are usually discouraged.

It really just depends on how rigid a definition you or your instructor has of Parkour, but in the truest form of Parkour, it's really about efficiency, not aesthetic.

David Belle, the founder of Parkour, has clarified in public statements that Parkour differs from arts like Free-running because of the differing philosophies on what is most important.

Parkour is about overcoming obstacles through improvisational movements which emphasise getting from point A to point B, not adding flair or unnecessary style to such movements, which, through their fluidity and ease of movement, should be beautiful enough so as to make aesthetics wholly excessive and unnessecary.

Lastly, Belle has also stated that the foremost purpose of Parkour is to help others, specifically using an example of the possibility of a traceur to help rescue someone who is trapped inside a burning building. Aesthetics don't fit into this example, nor do they seem to fit into the ideal of the founder of Parkour himself.

You can incorporate aesthetic moves into your own Parkour training as much as you'd like, but it isn't true to the ideal nature of Parkour.

Additionally, here is a quote from David Belle:

"Understand that this art has been created by few soldiers in Vietnam to escape or reach: and this is the spirit I'd like parkour to keep. You have to make the difference between what is useful and what is not in emergency situations. Then You'll know what is parkour and what is not. So if you do acrobatics things on the street with no other goal than showing off, please don't say it's parkour. Acrobatics existed long time ago before parkour." - David Belle, Creator of Parkour.