Juicebox has no built-in support for displaying Instagram images (like it does for displaying Flickr images).
It might be possible to do so via the Instagram Graph API (it looks like they are currently in the process of deprecating their Instagram API Platform) but it looks like it might be a rather complex project.
Even if you were able to use the Instagram Graph API to fetch a list of images to display in your gallery, you'd still need to write a script (in PHP or another server-side scripting language) to dynamically generate a gallery's configuration file (in either XML or JSON format) from the data gathered via the API.
All things considered, it would not be a quick and easy task (if at all possible).