Sounds like it's happening for a few people now, on a number of mobile devices. We'd like all of you to try the following:
Tap the three dots > Share > Instagram Story. It should be the second option on Android and the third on iOS.
If you're not seeing this, be sure to reinstall not just Spotify, but Instagram too. If you see the option to display more sharing options, always open it to check if it's at the bottom of the list.
If you then see the option to share through Instagram after that, you should see the pop-up 'Spotify wants to open Instagram' in the Spotify app. You'll then be navigated to Instagram, where you can preview the songs before clicking 'Send to >'.