Yeah the interface in the Kids app sucks. The way to do it is from your own phone. Use the "share" feature and choose "with kids". It takes a lot of taps to share a channel, that could be improved for sure. But if you share good channels as you come across them then over time you'll build up a great library of content for your kids.
The UX is a complete fail, my comment having a moan about it all has over 90 upvotes now, yet I'm wrong. But the reason I'm wrong is because they've made it painfully hard to manage.