If you receive the error message "No device found." upon providing your Apple ID credentials and optionally providing the correct 2FA code, then it may be due to one of the reasons as listed below:
Incorrect Apple ID
You must use the same Apple ID that has been used on your child's device to log in to iCloud. Please note, sometimes two IDs are associated with the same device - one is associated with iCloud and the other one is associated with AppStore. You must use the one associated with the iCloud.
No Recent iCloud Backup
If your device has never been backed up to the iCloud, you will receive the no device found error message upon entering your Apple ID credentials. Please create a new backup of your child's device before proceeding.
Go to Settings -> [ user name ] -> iCloud -> iCloud Backup -> Back Up Now
Once a new backup has been created, you must wait at least 4 hours before you try to add the device again. This is because of the processing time taken by Apple servers to set up your first iCloud backup.