React Native: fetch request failed with error - TypeError: Network request failed(…)

Since your Android device has an IP of its own, you need to point the URL to your computers IP address instead of just localhost. For example fetch('http://192.168.0.2:3333/').

Use the reverse command of the Android Debug Bridge tool (adb):

adb reverse <remote> <local> - reverse socket connections.
                               reverse specs are one of:
                                 tcp:<port>
                                 localabstract:<unix domain socket name>
                                 localreserved:<unix domain socket name>
                                 localfilesystem:<unix domain socket name>

For example:

adb reverse tcp:3333 tcp:3333

This makes localhost:3333 accessible from your device. You can also use different ports. For example:

adb reverse tcp:8081 tcp:3333

This will redirect the device port 8081 to the local port 3333.