First, head over to Settings on your iPhone. Next, tap General, and then tap Accessibility. From there, you'll need to toggle the Zoom option on.
This now allows you to zoom in on any app using three fingers. You'll need to double-tap the screen with three fingers to get it to work, and it requires a bit of practice.
The best way to master the new gesture is by starting with your thumb and two fingers closely together. After a quick double-tap with those three fingers, slowly splay them outward, similar to the traditional pinch-to-zoom motion.
To zoom back out, repeat the double tap, but this time start with your three fingers separated and bring them back together.
And you're all set! You'll now be able to zoom in on Instagram photos, though of course this doesn't mean the quality will be the best, but you'll at least be able to take a closer look.