If I reside in the Charter Township of Flint, do I file as a resident in the City of Flint?

No.  You are a resident of the Town you live in.  When you answer the questions in TurboTax accurately it will assign residency accordingly.

The City of Flint, by ordinance, collects a local income tax of 1% from residents and 0.5% for non-residents who work within the City. The Income Tax Division is responsible for administering the City's Income Tax.