It's possible to deploy Flarum on any server that meets the system requirements, local or on the net. For reference, they are the following:
A web server: Apache (with mod_rewrite), Nginx, or Lighttpd
PHP 5.5+ with the following extensions: mbstring, pdo_mysql, openssl, json, gd, dom, fileinfo
MySQL 5.5+
SSH (command-line) access
Note that PHP 7.0 compatibility is still being worked on.