Logout using link (without nonce)

This will disable nonce checking for logging out – on your head be it:

add_action( 'login_form_logout', function () {
    $user = wp_get_current_user();

    wp_logout();

    if ( ! empty( $_REQUEST['redirect_to'] ) ) {
        $redirect_to = $requested_redirect_to = $_REQUEST['redirect_to'];
    } else {
        $redirect_to = 'wp-login.php?loggedout=true';
        $requested_redirect_to = '';
    }

    /**
     * Filters the log out redirect URL.
     *
     * @since 4.2.0
     *
     * @param string  $redirect_to           The redirect destination URL.
     * @param string  $requested_redirect_to The requested redirect destination URL passed as a parameter.
     * @param WP_User $user                  The WP_User object for the user that's logging out.
     */
    $redirect_to = apply_filters( 'logout_redirect', $redirect_to, $requested_redirect_to, $user );
    wp_safe_redirect( $redirect_to );
    exit;
});