Instagram is appealing to people because in part it offers instant gratification and because it offers information in a visual format. A lot of students are bombarded by information in the form of text; putting things in a visual format is appealing. Also, posts on Instagram can bleed into other social networks and draw in additional viewers.
For secondary school students, Instagram could be incredibly useful in documenting and reflecting on out-of-classroom experiences, especially field trips. This is challenging in social science, since a lot of historical museums don't want visitors to take pictures or even bring their phones onto the premises. Paloma Valley's entire sophomore class goes on field trips to the Museum of Tolerance, but the MOT has metal detectors at the entrance and encourages people to leave their phones and cameras behind when they enter, which is incredibly disappointing in the context of this idea. However, I can see Instagram having a practical application for science classes that are going to more interactive out-of-classroom experiences. It is a way to ride the river of technology rather than fight against it.
Thinking even beyond instructional uses, the idea of using Instagram to connect to alumni can be used in a high school setting. Photos which show off the construction of new buildings, new events on campus or academic and athletic success can be used as a hook to get alumni who have not thought about or visited their high school campus in years to revisit the idea and possibly make some sort of contribution.