Roku does not write the apps, other than The Roku Channel. You will need to contact Spotify to see if they will make a special Kids version. From what I can see, it's only available for Android/Apple phones and tablets. No TV devices. Checked on a Google TV, and not available.
You can look for info or ask here:
https://community.spotify.com/t5/FAQs/tkb-p/Spotify-Answers
