Kaomoji App requires that each user in a team to individually "add" it for it to work properly for that user. If your team only allows admins to add Slack Apps, then an admin must perform the following steps to allow you to add Kaomoji App.
Have your admin (let's call her Melissa) add Kaomoji App to your team:
Then, have Melissa navigate to your team's App Management page, and click the Approve button for Kaomoji App, to move it from the Restricted Apps section to the Approved Apps section:
Finally, approve Kaomoji App again for yourself (you can use the Add to Slack button for yourself as well):
Done! ＼(^o^)／