How to hoste Sub-domain on Other hosting company:
In my case, I decided to host my forum on Bluehost hosting, and keep my main blog on WPEngine only. This way, I will avoid the huge charges of WPEngine (Their Billing plan works on number of visits), and this will make more sense in term of server load. Here is the exact steps I followed, and it will work with almost all the hosting and domain registrar.
In my scenario: My Domain is hosted on ShoutMyDomain and blog is hosted on WpEngine. And my goal was to host forum.shoutmeloud.com on Bluehost hosting.
