Soon you might be able to "regram" on Instagram without using a third party app

"We’re always testing ways to make it easier to share any moment with friends on Instagram."-Instagram spokesman
To regram a post, choose a public, permanent post from your feed. Tapping on a button, you embed it into your Story. You can choose to highlight the author's name, change the size of the original post, add your own personal comments, and use Instagram's tools to play around with the image. Tapping on the embedded post once it is posted on your Story will bring up a "see post" button. Anyone who clicks on that button will get to see the original feed post. Users who don't want their posts showing up in someone's Instagram Story can decide to opt out of the feature.
Instagram is testing a new regramming feature. The original post at left is embedded in a user's Story
source: TechCrunch