I set up an IFTTT.com recipe that creates a post on this blog every time I post a photo to Instagram. It works pretty well.
The photo posted here is actually a link to Instagram, so I guess if anything ever happens to the external link function on Instagram, these blog posts will have broken image links. I suppose if Instagram shuts down, I'll have to download the images and redo the links. I guess that could be time consuming if I have a lot of them. But, I'll worry about that when the time comes.
The only other issue is that the linked photo is a little too big for the normal post format. This means if I bring the site up on a mobile device, the images look all wonky. My current fix is to manually adjust the linked image to the right size. For now it works. Maybe later I will try to find a way to automate the fix. Or perhaps there is a way to fix the IFTTT recipe.