To be honest I'm really not sure how I should look at a question like this. I did this so far:

0.6390 g of AgCl * (35.45g Cl / 1 mole Cl) = 22.65255g Cl

I'm not sure if that is a useful step or not or what the next one shall be that I take. Any guidance is appreciated.

No its not a useful step and I have no idea what you are doing here at all.

Think about it again you have a known weight of unknown composition.

ZnCl2 (aq) + 2 AgNO3 (aq) -> 2 AgCl (s) + Zn(NO3)2 (aq)

From this equation you know that for every mole of ZnCl

_{2} in the sample you'll get 2 moles of AgCl solid.

You are told the sample gives 0.6390g of AgCl.

How many moles of AgCl is that.

How many moles of ZnCl

_{2} does that mean were in the sample?

What is the weight of the ZnCl

_{2} calculated from the no. of moles?

That weight of ZnCl

_{2} divided by the sample weight give the %ZnCl

_{2} in the sample.