So before you put your fathers sim from his Android into your old iPhone 6s, you completely prepared the phone for a new user per the directions in this link? --> What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support
If you didn't do this, and the phone is still tied to your Apple ID, you are actually trying to facetime yourself, which as you now know won't work.
Once fully wiped and ready for a new user, your father should set up the 6s with his own Apple ID, then set up facetime and iMessage with his cell phone number. Then you'll be able to facetime your father.