We (the developer) don't get any data. Your data doesn't leave your browser, aside from you sending chat messages and things related to chatting, of course.
There's no telemetry, analytics, or home server.
Currently (v5.x and before), when you start the application and "log in", it connects you to a seed node, provided by nkn.org (https://www.nkn.org/), to find other nodes in the network, and some other queries, like sending transactions, are also directed at that seed node.
All data that leaves your browser is end-to-end encrypted, like the chat messages and transactions.