It depends a bit on your theme how to tackle this, because under most circumstances you cannot just change the featured image without writing a plugin.
If you’re experienced with writing WordPress plugins (and Instagram’ API) you could write your own plugin that replaces the featured image.
I would rather recommend using an existing plugin – the first I googled was Instagram Feed by Smash Balloon, which looks like it can do what you need. Using that plugin I would not show the featured image but instead use the Plugin’s shortcode in order to show the right Instagram feed for your product.