This is a simple approach to check whether a user has commented on the post, or not. If they have commented on the post, then disable comment form.
global $current_user;
$args = array('user_id' => $current_user->ID);
$usercomment = get_comments($args);
if(count($usercomment) >= 1){
echo 'Comment form disabled';
} else {
comment_form();
}