How do I make a Japanese-style anime (like Naruto or High School DxD), with Adobe Animate?
Learn how to draw frame-by-frame animation without Animate.
Then do it with Animate.
It's a little like asking how to build a specific style house. What skill level are you at with drawing? What you're asking is a based entirely on style (drawing and animation). To be blunt, draw in that Anime style, and then animate in that style. But if you are asking technically how...then you need to learn the basics of symbols and the timeline and for that there are several tutorials available via the start screen or on the Adobe Animate product page or YouTube.
Making an anime takes much more than knowing a single software. You're gonna need to know how to draw mangas and how to animate very well. Among lots of other skills, like storytelling, composition, colouring, and so on.
But anyway... I think you can start by seeing some pros in action.
Wakfu is an anime from Ankama Studio that uses Flash (or at least used at some point) as their main drawing and animation tool.
Unlike most animes, Wakfu mixes frame-by-frame and puppet animation to bring characters to life.
There a lot of videos on YouTube showing how the studio artists work.
Playlist from Ankama:
Making of (1):
Making of (2):
DOFUS monster animation:
Write a script.
Design your characters.
Cast your actors.
Record a radio play.
Work out your poses and time them to the radio play.
Animate the in-betweens.
Decide if you want to finish in Animate or export your scenes to Premiere Pro.
Assemble your scenes (refine story as needed, make sure scenes hook-up)
Compose your score and add sound effects.
Add effects to visuals as needed.
Create your title cards and credits.