Twitch discontinued the Password Grant Flow, so unfortunately they will not grant any additional applications access.
As for how to go about implementing authentication on a mobile device, you would probably need to launch a local, high-port web server on the mobile device, as Twitch doesn’t support non-http(s) URI schemes that mobile devices support.
You could then configure a redirect to http://127.0.0.1 on whatever port you’ve bound to in order to grab the access code and request a token.