For beginners, tactics are utmost important. So you can create some tactic puzzle collections, and put them onto the device. You can get puzzle pictures from Facebook, Google+, Pinterest, or chess tactic websites. It's not difficult to accumulate thousands of puzzles, which is enough for your child to kill some free minutes. A puzzle picture is perfect for a smartphone screen.
You don't need any fancy apps. Just pictures, and a simple free app to show pictures. I am using QuickPic on Android.
Another help beginners need is coaching. You can also collect chess videos so your child can watch at any time. You can find them on Youtube, on chesslectures.com, and on ICC/chess.com, if you know how to download them. Again, a simple free video viewer app is enough. I am using MX Player on Android.
To transfer picture or video files from your PC to smartphone, I definitely prefer Android to iOS, which is much more intuitive.