I think YT auto suggests based on the usual factors - viewer past viewing habits, top videos from top channels, etc. I don't think there's a way to get in there per se.
For example I installed the YT kids app on one of our devices, and logged in with the google account of my daughter. The videos suggested were from channels she watched previously on another device using the "normal" YT app. We even saw our own videos appearing, as the kids watch those.
So basically if your subscribers watch your videos on the PC or regular YT app, then when they install YT kids, they should still see your videos recommended. The more they watch them, the more they should appear, I would assume.