custom wordpress logout button(wp_logout_url) in wordpress
<li class="menu-logout"><a href="<?php echo wp_logout_url(); ?>"><span><i class="fa fa-sign-out"></i></span>Logout</a></li>
Or
<li class="signOut"><?php wp_logout(); ?></li>
add_action( 'wp_logout', 'auto_redirect_external_after_logout');
function auto_redirect_external_after_logout(){
wp_redirect( 'http://redirect-url' );
exit();
}