How can I set my iPhone's time to that of a NTP server?

You can set it to the minute but I am not sure you can set it to the millisecond. Go to settings>general>date & time - turn off set automatically. Next go to settings>privacy>location services>system services - turn off setting time zone.

Once you have done that you can set your time the way you want it. Having those on though keeps your device synced with the NTP server.

I would actually leave the phone on automatic time setting then. It will get its time signal from cell towers, which in turn get theirs from NTP servers. Cell carriers don’t run their own atomic clocks - they use available ones like the Naval observatory’s or NIST’s. Just hook your computers into a good one too (I like tick and/or tock .usno.navy.mil just for the names 😝 )

I just checked my iPhone X and my Macbook pro and they are synced with the NTP time to the second.

They are already synced. You have to understand that electronic deficiencies affect the time by milliseconds. When you get into millisecond syncing you are talking precision instruments.

The Navy website is where I got my info to answer this question. I was a Marine so I use all the Navy resources I can when possible.

There is an app called US Official time in the app store.