Checking for User Role in Views Field with Twig
First, you should not do security by role.  It should be done by checking for a permission.

In general...Twig gets passed a user variable from Drupal that can be used for this.  There is a hasPermissions method.  Here's a sample code snippet.

  {% if user.hasPermission('administer eck entities') %}
      &lt;a href='{{ add_url }}'&gt;Add tab&lt;/a&gt;
  {% endif %}


If you must use roles, there should be an hasRole() method on the user object that is passed in.  (See User Object api docs)

For Views:

Views has limited twig like support in the GUI but does not support all the functions of the underlying twig functions.  To check for user permissions in a header, you will either need to use the hook_preprocess_views_view() or create your own view specific template, e.g. views-view--view-name.html.php in your theme. You will need to process the header (or footer) variables in these to get the permission specific info into the view. 

If you want to limit specific fields, you can use the field specific hook and templates as well.