Instagram is providing the feature of adding music to Instagram Stories. If you want to make your music available for the public in the app, you must distribute it to Facebook Rights Manager.
Instagram is linked to the Facebook Rights Manager catalog, from where the application gets the music that you can find available for sharing in their users' stories.
You can check the first step in knowing how to add a story or how to add music in the story going to "What are some tips for uploading, recording and editing my story?".
If your songs are not displayed in Instagram stories but you have previously distributed them to Facebook Rights Manager channel, please, contact email@example.com.
Are we collecting royalties from our music being shared in Instagram stories?
No, for the time being Facebook Rights Manager is not monetizing. It offers a legal protection in Facebook and, as it is connected to Instagram, it allows the app users to add the songs distributed to its database, providing visibility for the artists.