Before you try to turn on Developer Mode, make sure you have an APK signed with your device's OSIG file installed on your device. Otherwise, it will show "You are not a developer".
Steps:
1. Install custom APK signed with your device OSIG
2. Open Settings - Applications - Application Manager
3. Look for Gear VR Service
4. Select Manage Storage
5. Tap VR Service Version until you see "You are a developer"
6. Turn on Developer Mode
That's it!