Sociolatte

Instagram have completely removed support for Twitter Cards and therefore users cannot share Instagram photos on Twitter. Only a link gets shared and no photo. If you are one of those people who's used to seeing those nice Instagram photos in your Twitter feed or Mobile Interface. That ability is gone and Twitter on the other hand have released their own photo-sharing with filter effects feature. If however you still want to be able to view Instagram photos on Twitter there is a Chrome Extension for that. With the extension you will be able to view photos in your Twitter stream and users Photo Galleries.

How to view Instagram photos on Twitter
You will need to download and install the InstaTwit Chrome Extension on your device.
Once installed on your device all you need to do is to refresh your Twitter page and all the Instagram photos are visible.

So all those Instagram photos and user galleries become visible and users have the ability to view all of this right from within Twitter.

InstaTwit Chrome Extension