This should reset the i OS App Store cache and your issues should go away.
Large numbers of people have installed i OS 10 and then hit a snag of some kind.
If these troubleshooting steps don't help, please contact Apple support.
If you’ve been having problems with the i OS App Store for the i Phone, i Pad or i Pod Touch, there is a simple and easy fix that may be able to solve your issues.
The latter can be done by holding both the lock button and the home button together for about 5-7 seconds, while the former can be accomplished by navigating to the “Featured” tab in the i OS App Store and then scrolling all the way to the bottom of the page and clicking on your Apple ID email.
Resetting the i OS App Store cache trick also works with the i Tunes Store app, and the Apple Watch app as well.
You can reset the i OS App Store cache by tapping at least ten times on any of the tab bar item, including “Updates,” “Search,” “Explore,” “Top Charts” and “Favorites.”Apple has adopted a fast beta/release cycle with i OS 9, with two major updates since the operating system’s initial release in September 2015.
i OS 10, the newest operating system for the i Phone and i Pad and a free update for anyone with an i Pad 4 or later or an i Phone 5 or later, offers a raft of new features and various tweaks to the interface: but it's not all good news.
After you restart your phone, try installing the Instagram app again.
Some people have reported that syncing their phone with i Tunes and reinstalling Instagram from i Tunes helps with this process.