Hi Alex,

The following link is for direct logout:

http://example.com/index.php?option=com_users&task=user.logout

The following code will display a Login link to guests, and a direct Logout Username link to logged in users:

$user = JFactory::getUser();

if ($user->guest)
{
    echo 'Login';
}
else
{
    $userToken = JSession::getFormToken();
    echo 'Logout '  . $user->username . '.';
}

Know more - joomla.stackexchange.com/questions/5703/direct-logout-link 

You can try also Joomla component - extensions.joomla.org/extension/quick-logout/ 

Best Regards
AppClave Team