This app was mentioned in 4 comments, with an average of 4.75 upvotes
I haven't tried this, but a guick googling has given me the idea that you could setup Nginx with the RTMP module and set it up for recording incoming streams. Then use an RTMP Camera app on your phone to stream it to your server. I'm afraid it's probably not the most simple thing to setup and I can't give you step by step instructions, but here's the stuff I found, which might be able to do it: * https://github.com/arut/nginx-rtmp-module * https://play.google.com/store/apps/details?id=com.miv.rtmpcamera
Hi! This is great - in looking at this I came across the Nimble Streaming Server. I just insatalled it via using the suggested commands in terminal, and I now want to explore if I can use https://play.google.com/store/apps/details?id=com.miv.rtmpcamera as an app that anyone can use to stream to my server in Nimble, and then bring that into OBS...that seems logical to me, but not sure if it works that way.
I know that the "RTMP Camera" app for android will run in the background. It even runs with the screen turned off. I don't know if IOS allows for the kind of multitasking you want.
https://play.google.com/store/apps/details?id=com.miv.rtmpcamera&hl=en
EDIT: Looks like the first one supports streaming while it's in the background, so you could read chat while streaming.
You might need to have the ingest URL formatted to: rtmp://live-iad.twitch.tv/app/{stream_key}
If that doesn't work, let me know and I'll dick around with it. I had something working about a year ago, but it was on my previous phone. Looks like the apps have gotten better since then.