What is the most appropriate approach/tool in the Adobe CC suite for creating animated diagrams for use in a technical video? I'm working on a technical video (in Premiere Pro) describing some work we've done in an academic setting, akin to a presentation one might give at a conference. There are recorded video elements that I'd like to overlay with animated diagrams describing how things work.

What's the best way to achieve this kind of thing? I ran across a video tutorial that creates a simple animation using the title creation features of Premiere Pro, but that seems like the wrong tool.

I've got an active CC membership to work with. Maybe I could create a diagram and animation in Animate (previously Flash) and export it as a video, with alpha channel, to overlay. I have limited experience with Flash from years ago. I assume After Effects can do this sort of thing, but I've never worked with it myself. I'm very comfortable in Photoshop and Illustrator since most of my work in CC involves photography and still technical drawing/writing.
After Effects is probably your best bet, as it integrates seamlessly with Premiere and Illustrator. 

Create your diagrams in Illustrator, import them into After Effects, and convert them to shape layers. You can then animate them, and add the AE compositions to the Premiere project.