Allow users to publish their own Instagram profile on a page / site?

We are looking for a way for end users of a site to be able to publish their own recent profile posts in a grid on a site we produce, with just a few clicks and without any formatting options. The output would be similar to LightWidget or EmbedSocial

Until now, we have only seen APIs that would allow the user to go through the admin area of ​​a third party utility to which he should register. or even pay, and via a complete user interface that we would not want users use.

Does something like that exist? The same is it possible? I've sent emails to a few companies that offer these services and they do not respond.