I believe that the first step(s) and its not an easy one for beginners (i'm one) is that you need to establish a network first.
i.e A means for any mobile device to connect to a LAN network where your Raspberry PI Zero can receive network communication.
Steps (by no means perfect but will give you some idea how I would go about it)
1) Set up a LAN of at least 2 Raspberry PIs. (i.e Wired LAN network)
2) Make the First Raspberry Pi a Wifi Hotspot (a quick search of the forums "Wifi Hotspot")
https://www.raspberrypi.org/documentati ... s-point.md
It will still be part of the Wired LAN because your using the Ethernet Card on the Raspberry Pi, but also the "Wifi Card" will be a second network on the same Raspberry PI
3) Get the Wifi Network clients(phone) to see and communicate with Wired LAN network (Raspberry Pi Zero) clients via a Bridge.
The Bridge is setup on the First Raspberry Pi i.e the one withe the Wifi Hotspot installed/configured.
4) Test/Perfect the Connectivity of connecting the Phone to the Wifi Hotspot, which should be able to see and communicate with Wired LAN clients. (i.e share files for example)
A quick google of "raspberry pi chat server", and I found this, You could take a look at this, I don't know anything about it, but if you can communicate between the Phone and your Wired Lan, then you can add a Chat Server/Service to complete the process.
I hope that helps.