disclaimer: simply my interpretation based on existing work out there, i am not an attorney and nothing is meant to be construed as legal advice.
There are plenty of apps which use the name Twitch such as “Ace for Twitch” and “Twitch Dashboard” etc.
There are others which play on abbreviations such as “TChat” “TwIRCh” etc.
If the APK is not for profit, my best guess would be that you can do similar to those referenced by me above.
If the APK is for sale and profit, the answer is no.
I would be very wary of using the Twitch logo, however.
Many uses can probably be filed under the following ‘allowed usage’ in the second link given by george in his response:
“for statements of compatibility (ex. “Compatible with Twitch”);” I am not any kind of attorney or legal authority but many uses would likely fall under a compatibility clause, such as the above referenced “Ace for Twitch”, etc.
Again, not an attorney or legal expert, but these sorts of company-written documents are generally stricter than they can actually enforce, such as this one: “Do not register a domain name containing Twitch or any similar variations, which includes any misspellings or transliterations.” That is clearly non-enforceable and is done all the time with every single popular website on the internet, so long as you’re not actually imitating the parent website itself with the website content. (i.e. dont make twcith.tv and copy the twitch layout and functions. But if you are Time Warner Cable of Ithaca and offering streaming TV services, this is obviously far above and beyond twitch’s scope of authority, even though they claim otherwise in the documents, lol)
Anyway, long story short, I would simply use a name like “____ for Twitch chat” or “Twitch channel browser”, etc. You are allowed to say or imply you are compatible with Twitch services.
I would not use the Twitch logo.
Also, the two links george gave are meant to work in tandem with each other, so if one says it and the other doesn’t say the same, it doesn’t matter, only one of them has to say it.
Check out the google play store (I assume you will be publishing your apk there) and use others’ names as an example. Here’s an example search in the google store for other similar apps, try searching for things like “Twitch channels” “twitch” “twitch browser” etc. [https://play.google.com/store/search?q=twitch%20chat&hl=en]