Kiddie Tax Residence & Filing

Kid's unearned income (from sale of stock, not dividends) was >$1350, so he needs to file (even though it was <$2700 so he owes $0).

How do we determine the kid's state of residence? If it's the physical domicile, no requirement to file if <$3270 in this state, but I figured it was worth asking before we PCS to another state.

Also, any specific way to file that's better than another for a military brat? I'm leaning toward the Free Fillable Forms directly with the IRS, but could use one of the Free File Alliance providers.