It doesn't look like much. There is a Button and if you click it, it shows you the balance of a hardcoded address. The application also loads an account from a hardcoded json address file and prints that address on clicking the button.
This example is just a simple Proof of Concept, so the code is not pretty nor is it supposed to be re-used anywhere else.
Run with npm start. Run on android with npm run android. After running, it takes some time to connect to nodes and sync with the main ethereum network - before it is connected to any peers, the button does not work.
This project was bootstrapped with Create React Native App.