Power supply architecture for energy metering IC (HLW8012)
The important thing to remember in this design is that "live" (the hot wire) is also ground to the circuit: -



Live directly connects to the shunt resistor and this means that live is also GND (0 volt reference) for the chip.

You can swap incoming live and neutral connections and it will still work but now neutral becomes the 0 volt reference for the chip.

So, providing you design the "power supply" section to respect the reference 0 volts for the circuit you are fine. 

If you choose neutral as the reference you can utilize this design to measure power in two (or more) phases providing you connect the current shunts to a star point at neutral. You should also be able to use a common "power supply" section but, because I don't read Chinese, I have some doubts about chips input common-mode range for the shunt differential inputs. I would be cautious here.