Thanks Nikonian.
I called Nikon Tech Support and was given a very simple answer, which is consistent with your response:
Because the D3400 does have the Save Feature built in, changes to the flash setting within the Auto mode or any of the Scene modes (Portrait, Child, Close-up, Night portrait) are temporary. (Landscape and Sports are flash off only.) They apply to the pictures taken before the camera is shut off. Once the camera is shut off, the settings are lost and mode reverts to Auto.
In the P-S-A-M modes, the default is for the flash to be disabled. Any changes to these via the ‘i’ menu are retained even after the camera is shut off.
The “No Flash” mode is essentially the Auto mode with flash disabled.