Find Proxy IP address used by Android app
The easiest way to monitor Android internet traffic is to connect it to a Wi-Fi network and run Wireshark on the router. That way, you can do whatever you like on the Android device while watching the packets go past on the Wi-Fi router.

An on-device solution can be less convenient, because you have to do the activity you want to monitor, then switch to the monitoring app to see the results. In addition, you need to have root on the device to monitor other apps' network traffic. In some cases this can change the behaviour of the app you want to monitor, though I don't expect that'll be a problem for you. Network Log is an open-source example of an on-device network logging/monitoring app.