Can I trade in a locked iPhone from Vietnam for a new one in the US?

No, you cannot trade-in your carrier locked iPhone in the US. You must fulfill the requirements your Vietnam carrier has on your iPhone and then request they unlock the device.

The iPhone cannot be carrier locked in order to trade it in, in US.

There are several types of locks on the iPhone. Which one are you referring to? Do you mean you cannot get into the phone as it is Activation Locked?

Are you saying that your phone is carrier-locked?