What's the simplest way to get streamer's permission?

I say to the streamer “click this link and then hit accept”

"this link’ is a link to my website/tool, that redirects to Twitch, they hit accept.
They come back with a ?code which is exchanged for an access and refresh token.

Theres nothing simpler than that, as that is how oAuth works.

Not sure what you mean here.

A generated auth token has a client ID attached to it.
And both need to be specified when you call the API.