build.gradle

dependencies {
  ...

  + implementation "com.squareup.okhttp3:okhttp-brotli:4.7.2"
}

fetch.ts

async function fetchData() {
  return await fetch('https://www.google.com', {
    headers:
      // It is important that the Accept-Encoding key is not present on Android.
      // Null / undefined won't work.
      Platform.OS === 'ios' && parseInt(Platform.Version as string, 10) >= 11
        ? {
            'Accept-Encoding': 'br,gzip',
          }
        : {},
  }).then((res) => res.text());
}

MainApplication.java

+ import com.facebook.react.modules.network.OkHttpClientProvider;
+ import okhttp3.OkHttpClient;
+ import okhttp3.brotli.BrotliInterceptor;

...
  
public void onCreate() {
  super.onCreate();

+   OkHttpClientProvider.setOkHttpClientFactory(() -> {
+     OkHttpClient.Builder builder = OkHttpClientProvider.createClientBuilder();
+     builder.addInterceptor(BrotliInterceptor.INSTANCE);
+     return builder.build();
+   });

  ...
}