In my experience, Having a custom DNS (Al-zif/NightKing/Crono) etc does not allow it to load. Try re-setup your Wifi on 'Easy' and try the YouTube app again. Good Luck!
UPDATE : So, I've tested it out - Removing the DNS, Letting it load up once (First time) Then re-setting up your Wifi to work with DNS - Also sorts the issue & YouTube Loads up fine afterwards.