digitalissimo

If you need to get the information from another site or your site using JSON API (https://wordpress.org/plugins/json-api/) you can use this plugin. 
For slideshow this plugin use Cycle2 (http://jquery.malsup.com/cycle2).
<h4>Shortcode</h4>
<pre><code>[getapi url="www.mysite.com" limit="5" type="[CYCLE or LIST]"]:
</code></pre>
<ul>
<li>
url: url before ?json=get_recent_posts
</li>
<li>
limit: number element of json result
</li>
<li>
type: “Cycle” is a slideshow of thumbs or “List” is the list of post titles
</li>
</ul>

Get Json Api

Retrieve the results of the API of a site that uses the plugin JSON API

Ali Qureshi

JSON API Cincopa plugin extends the JSON API Plugin with a new Controller to provide Cincopa Easy Albums Listing for any user. This plugin is for WordPress/Mobile app developers who want to use Cincopa Easy Albums Plugin in conjunction with JSON API plugin as media gallery for their mobile app.
Features include:
<ul>
<li>Easy Albums Listing</li>
<li>Easy Albums Items Listing</li>
</ul>
The plugin was created to make available Cincopa Easy Albums Plugin Media listing for mobile apps via JSON API Plugin.
Hope this will help some.
For details, please check this: http://www.parorrey.com/solutions/json-api-cincopa/

JSON API Cincopa

Extends the JSON API Plugin to allow RESTful Cincopa Easy Albums Listing for any user

Get Json Api vs JSON API Cincopa