Toriko I'm running out of ideas. There should be a message somewhere.
Maybe try altering the index.php or add another php file that should return some text and check if this is correctly handled by php-fpm, so we can figure if it's PHP related or Flarum related.
Did you follow a guide to install that server ? Didn't you already install some form of PHP along with nginx ?
Were you really able to install php7.2 on Ubuntu 16.04 ? The default repos certainly don't have it, did you add a repo for more recent php ? My example config is copied from my server running php version 7.2, it might not apply to the php version you installed. But if that part is incorrect you should encounter a 500 error from nginx... That config goes inside the server directive, but again if you did not put it in the right place I'm sure you would be getting an error.
Doesn't hurt to do a full restart in any case.