LinkedIn says the following on its JSAPI reference page:
The API reference lists a number of actions you may wish to perform and provides examples of each of them. Some of the available actions include initializing the framework, accessing data about LinkedIn members (the bulk of the API), rendering login and share buttons, authentication, event, and UI features. I’ve provided a couple of examples below to give you a feel for what’s possible.
First, if you want to use the JSAPI in your browser app, you will need to have the user login. This gives you access to their member information. To create a “Sign in with LinkedIn” button like this:
<script type="IN/Login" data-onAuth="[onAuthCallback]" data-onLogout="[onLogoutCallback]">
where you may use the templating capabilities described in the reference page in place of the template placeholder above.