Since YouTube Kids is for kids, no wonder why Google has added some annoying background music and sound effects while browsing in the app. To disable sound effect on YouTube kids, do as follows:
1. Open YouTube Kids on your Android device
2. Tap the lock icon on the bottom right (while holding the device in landscape mode)
3. Type the random digits shown on the screen as the password
4. Go to the Settings.
5. Under the Audio settings, make sure to unmark Background Music and Sound Effets.