Hi, HShankaran.
Welcome to the Apple Support Communities. We’re glad you decided to reach out about using iMessage and FaceTime on your dad’s iPhone. If we understand correctly, you created a new Apple ID for him, and you logged him into his iPhone 6 where he was able to send/receive text messages and phone calls, but you weren’t able to get either FaceTime or iMessage to work.
Does this sound correct? If so, are you still unable to get either to work? We’re asking because it can take up to 24 hours for either of those services to fully activate. If they aren’t working immediately after creation, you may need to wait for activation.
If you get an error when you log in similar to one of the errors listed in the article we have linked below, try the troubleshooting outlined therein.
If you get an error when trying to activate iMessage or FaceTime - Apple Support
Note that he will need to have cellular service activated on his iPhone with the ability to send/receive SMS messages to activate these services the first time.
All our best.