I’m looking for ways to do animation on painted cartoon character features. My current thought on the matter is to have one scene that renders the relevant texture bits for the character but I can’t figure out how to pipe the scene’s render result into the material texture. Am I approaching this wrong or am I missing something?
I don’t know if such a “pipeline” is possible… Any way, even if it’s possible, nobody in their right mind would do so. 
It would mean to re-render the first animation any time you do a change to the second animation… even if you don’t need to.
Instead, it’s better to render the first animation as frames and to use it as image sequence for the material in the second one.
To be thorough, I must also mention the possibility to use a video as source for your material… but just to say: Don’t.
Nobody in their right mind renders anything directly as video. And nobody choose deliberately to deal with video compression artifacts when it’s not necessary. Just keep your animations as frames as long as possible.
Needless to say that JPEG isn’t the appropriate format for… anything… Well, at least, not to store frames. Use PNG.
Okay, I’m just rendering it out into files then.