Add the download button and the open button to download or open profile picture and media in the posts, stories, and highlights in Instagram
< Feedback on Instagram Download Button
See pootz10's post, there he shows how to fix this in Firefox
Doesn't chang anything for me but even before it seems to do not work only on storys of private profiles.
Cross-Origin Policy of Firefox is blocking Story and Highlight downloads. Couldn't find a way to set exceptions to Firefox for Instagram yet :(