I've tested the image and it doesn't show up on my phone too, even after changing all available settings on Opera Mini.
Excerpt from the Opera Mini FAQ Page:
Opera Mini uses a transcoder server to translate HTML/CSS/JavaScript into a more compact format. It will also shrink any images to fit the screen of your handset. This translation step makes Opera Mini fast, small, and also very cheap to use.
My guess is that Opera mini fails while trans-coding certain type of images. I've tested other images, such as png, jpg and gif and they all display correctly.
After collecting more info about instagram images I've found out that their JFIF properties is:
JFIF Version 1.01
Resolution 1 pixels/None
If I convert the same image on photoshop Opera mini displays it correctly.
Based on this, I can assume that the problem isn't related with cache or amazonaws, it's in the relation between opera mini
and images with JFIF Resolution 1 pixels/None
I'm afraid I don't have a solution for you besides filling a bug report on the Opera Mini bug report page:
https://mini.bugs.opera.com/
I'm sure they'll look at it and it's your best chance to get this fixed asap.
You can also try posting on the opera community forum:
http://forums.opera.com/categories/en-opera-mini
Best of luck.