Enabling other phone in my account to use Netflix without giving login and password

Each user in your household must login to Netflix with the same userID and Password. 

You can assign a Pin number to each profile that must be entered to access the profile.  A second user would need to know the Pin number assigned to your profile to gain access to it.

Perhaps your question is more related to activating a new device than for logging in. I believe that what you described is presented when you activate a new device like a second phone.  But once it has been activated and automatically logged in, I believe you will need to enter userID and Password each time after signing out of Netflix on that device.