When asessing the cash flows of an investment in an NPV analysis,
should financing cash flows also be considered in addition to
operating and capital cash flows? For example, if bank financing is
required to undertake a project, then would the cash inflow and
associated principal and interest payments be present in the analysis?

No, financing cash flows should not be included.  The affect of
financing will show up in your cost of capital indirectly.  The cost
of capital should be calculated generally using the all costs (cost of
equity and debt of the corporation).  If you only take into account
the cost of the new debt, NPV will be over-inflated because the cost
of equity is normally higher than the cost of debt.