I have implemented Facebook App Links by following steps mentioned with Mobile Hosted API for the iOS app which is in Appstore.
When I test the App Link (http://fb.me/....) in browser or mobile, it doesn't redirect to Appstore.
However, I have tried it for some other App & it is getting redirected.
As I don't want others go through lot of R&D as I did. I am posting the answer myself.
As our App was available only for Indian stores, the Facebook App Link was not working.
When I changed the territory to worldwide & tested the App Link, it works. I observed that whatever Facebook link is given indirectly redirects to 'us' store.