The API from Twitch which you can use to query your followers, and pop the top one of the list, includes a logo, please review:
https://github.com/justintv/Twitch-API/blob/master/v3_resources/follows.md
In particular, the section “GET /channels/:channel/follows”
Each user object contains a logo of either null (meaning they have no logo) or the URL that points to their logo.