If its a plain text instagram wont notify other person that you took a screenshot. Other person will get know if you take a screenshot of instagram chat, when there is a picture sent. For example if other person sends you a disappearing instagram picture, then if you take a screen capture of that, then other person will be notified by Instagram. That you took a screenshot.

Maybe you also fall in the above scenario. Check whether you took a screenshot of a picture. You may read will the other person know if i unsend a message on instagram.