With the following snippet you can create a link or button with classes from a route. Use the setOptions() method to add the classes:
$link_options = array(
'attributes' => array(
'class' => array(
'btn',
'btn-primary',
),
),
);
$link = Link::fromTextAndUrl(t('Read more'),
Url::fromRoute('my_route', ['id' => $entity->id()])->setOptions($link_options));
$output = $link->toString();