How do I check the value of a Boolean field in a template file?
I don't know how you debug but I think from question contest that trying  node.field_checkbox.0.value might work. Or if you are working with views and use views_get_view_results function, try content._entity.field_checkbox.value or content._entity.field_checkbox.0.value 0 used if field is untranslated

Update for comment: 

function TEMPLATE_theme_suggestions_page_alter(&amp;$suggestions, $variables) {

  // Check it's a node page.
  if (($node = \Drupal::routeMatch()-&gt;getParameter('node')) &amp;&amp; $node instanceof \Drupal\node\NodeInterface) {
    array_splice($suggestions, count($suggestions) - 1, 0, 'page__node__' . $node-&gt;getType());
  }
}


with this code in your TEMPLATE.theme file drupal 8 suggest page--node--CONTENT-TYPE-MACHINE-NAME.html.twig (Undersores to dushes). and thats it, You might have {{ kint(node) }} or {{ dump(node) }} in your twig.