Get the users that my following users are following

You can use the implode function to concatenate array elements:

$get_the_following_users = get_user_meta($current_user->ID, 'following_users', true);
$meta_qssuery = ''; //initialise to an empty string
foreach ( $get_the_following_users as $following_user ) {
    $following_user = get_user_meta($following_user, 'following_users', true);

    if(!empty($following_user)) { //check if any data was returned
        $meta_qssuery .= implode(', ', $following_user).', ';
    }
}

echo $meta_qssuery;

This will leave an extra ‘, ‘ at the end of the string. This can be removed after the loop ends, or you can modify the loop:

$get_the_following_users = get_user_meta($current_user->ID, 'following_users', true);
$get_the_following_users_2 = array();
foreach ( $get_the_following_users as $following_user ) {
    $following_user = get_user_meta($following_user, 'following_users', true);

    if(!empty($following_user)) { //check if any data was returned
        $get_the_following_users_2[] = implode(', ', $following_user);
    }
}

$meta_qssuery = implode(', ', $get_the_following_users_2);
echo $meta_qssuery;