Yeah, the XBMC Youtube addon used to do subscriptions and the like, it was pretty nice, but I think it broke and the main developer abandoned it. Youtube-dl does support channels and resuming though so you could fairly easily just set up a cron job and use syncthing to get the videos onto your phone. No pretty GUI for that though.

I personally use an RSS Reader to handle my "subscriptions".

The YouTube-webpage also has an option to export your subscriptions to an OPML-file (which can then be imported into an RSS Reader): Log into your YouTube-account, then go to "Manage Subscriptions", and then at the bottom of that page, there's a button for it.

(This is how it worked a few months ago. I actually don't have a YouTube-account anymore, so I can't check if it still works like that.)

On Android, I personally use SpaRSS [0] with it, which does work quite well, but it being available on F-Droid was pretty much essential to me, so if you don't care about FLOSS, you might be able to find an RSS Reader which integrates even better with this setup...

[0]: https://f-droid.org/repository/browse/?fdid=net.etuldan.spar...