Twitch Brand assets as well as guidelines on their use can be found here: https://www.twitch.tv/p/en-gb/brand/
So for a simple button to connect their account you would just create a simple button, style it with Twitch purple, and add some text on it like ‘Connect with Twitch’ or something along those lines, maybe include the Twitch Glitch or the Twitch logo. It’s up to you what you do, just make sure you follow the brand guidelines.