That exact wording, “Where are you packing your bags to go?” would be understood by an English speaker, but isn't 'correct'. If coming from a native speaker, it sounds like they didn't complete the thought before speaking or are taking a short cut.
Taken literally, you're asking where the bags are going, implying without the owner.
To politely ask where someone is going after seen them packing, you could say:
I see you're packing bags, where are you going?
Where are you going? You're packing bags.
What are the bags for? Taking a trip?