How to apply styles to a child class in JSS

If btn is another class defined via JSS, then you need to refer to it using $btn.

See this part of the JSS documentation.

Here's some sample code that works:

import React from "react";
import ReactDOM from "react-dom";
import { NavLink, BrowserRouter } from "react-router-dom";
import { withStyles } from "@material-ui/core/styles";

const styles = {
  btn: {},
  active: {
    "& $btn": {
      backgroundColor: "#2A354F",
      color: "#fff"
    }
  }
};
function App(props) {
  return (
    <BrowserRouter>
      <div className="App">
        <NavLink to="/" activeClassName={props.classes.active}>
          <button className={props.classes.btn}>Link</button>
        </NavLink>
      </div>
    </BrowserRouter>
  );
}
const StyledApp = withStyles(styles)(App);
const rootElement = document.getElementById("root");
ReactDOM.render(<StyledApp />, rootElement);