A star-shaped icon will display next to the handle of the user and this is ultimately how it will appear:
Instagram also alerts the screen grabbers with the following message when they take a screenshot:
Interestingly, the aforementioned message will appear only once and Instagram won’t remind about it over and again. If a user miss it for some reason, he won’t be knowing that the other user is being reminded about the screengrabs.
It is worth mentioning that a user could still take screenshots without getting noticed. There are 3 ways:
1- Download Stories directly from Instagram website
2- Head over to Story Reposter without getting detected
3- While taking a screenshot, make sure your phone is set on a flight mode
Instagram is gradually rolling out this very feature and it would be available for everyone quite soon.