Instagram do not notify users if you take screenshot of their profile , stories or messages like Snapchat , If you use vanish mode in Instagram , Vanish mode is a mode in which messages got disappear when other person have seen message once . or if you close vanish mode .
You can turn vanish mode on by opening someone message on Instagram and then holding and moving up in bottom part of message . If you have screenshot in Vanish mode then other person will be notified like Snapchat , If you have screenshot in regular mode , then other person will not be notified .
