Recently I've been studying kihon from different karate styles to try and round out my understanding. It seems like most styles include a flying side kick in their kihon. Does it ever show up in a kata? I know it doesn't in any Goju kata, but I don't know the Shuri-Te katas. I'd love to see it in context because the more I look at it the less convinced I am it's even a kick. It looks more like a jumping Uchi-Mata or harai-goshi to me.
I trained Shotokan for a long time and now I'm in Goju, never did flying kicks not even once in any kihon and never seem in any kata.
I found this video helpful to understand this issue (it includes flying kicks), it doesn't mean we shouldn't use high kicks and stuff, it just means that if you want to kick better it may be a good idea to study Savat....
https://www.youtube.com/watch?v=sQUh5tVWd-E&t=2s
For those you need Taekwondo. In ITF Taekwondo a jumping side kick first appears in the pattern Chung Moo which is the pattern for first degree.
I once downloaded the WKF Karate app as a reference and of the four schools (Wado, Shito-ryu, Shotokan & Goju) I don’t recall a kata contain a flying side kick. A jumping front kick shows up in Kanku-dai (Kushanku) and in a couple of others, but that’s the only “flying kick” I’ve seen in kata. Also I don’t remember a jumping side kick in kihon either, some of worked on it individually, but not as part of a class.
I suspect that kicks like a flying side kick are more modern inclusions into karate from outside influences such as Savate. Another alternative is that if the kata are meant as manuals for self defence they may not have been included due to impracticality. It’s not a technique that can used at close range (grappling range); it’s something you might use to close the gap to your opponent but it is a fairly high risk manoeuvre.