In order to connect your YouTube account to your Moovly account you will have to add it in your Moovly profile.
To go into your Moovly profile, go to your Profile by clicking the avatar thumbnail in the right upper corner of your Dashboard:
...then select 'My Profile':
Within your Profile choose the ‘Integrations’ tab:
...at the top you will find ‘YouTube account’. Click on ‘Sign in’ and enter your YouTube login and password. Your account will now be connected.