It can be possible to generate an unsigned apk version for testing purpose so you can run on your mobile.
Initially i got the red screen errors as most mentioned here. but i followed the same which was mentioned here and it worked for me.
On your console from working directory, run these four commands
react-native bundle --dev false --platform android --entry-file index.js --bundle-output ./android/app/build/intermediates/assets/debug/index.android.bundle --assets-dest ./android/app/build/intermediates/res/merged/debug
cd android
gradlew assembleDebug
gradlew assembleRelease
And then APK file will produce on : android\app\build\outputs\apk\debug\app-debug.apk