is there a chance to display my instagram photos on my smugmug site like a blog?
Instagram does not provide a feed. I've tried several third party solutions but they all break eventually.
One is https://websta.me/rss/n/USERNAME
You can try adding that link in an rss feed on your SmugMug site but it may eventually stop working.
Free trial of feed produced by RSS.app seems to be working OK in a Smugmug Feed block.