This study endeavours to introduce an inventive hierarchical coupling methodology for evaluating the flight capabilities of polymer micromachined flapping-wing nano air vehicles (FWNAVs) using advanced computational tools. Furthermore, our objective is to provide a practical demonstration of FWNAVs in both tethered and airborne scenarios. These dual objectives represent the distinctive and pioneering aspects of this research. Such FWNAVs, which are insect-inspired robots, have a 2.5-dimensional structure. An FWNAV comprises a micro piezoelectric drive system and a pair of micro thin flexible wings. The drive system includes a micro transmission and a piezoelectric bimorph actuator. The flight performance of the designed FWNAV is evaluated using a hierarchical coupling approach, where the whole system is decomposed into a micro wing and a micro piezoelectric drive system. The coupling between these parts is modelled as one-way coupling and that between the micro wings and the surrounding air is modelled as strong coupling. In the one-way coupling analysis, nonlinear structural dynamic analysis is conducted for the micro piezoelectric drive system, where the dynamic response is transmitted to the micro wings via the Dirichlet boundary condition. In the strong coupling analysis, strongly coupled fluid-structure interaction analysis is conducted for the micro wings and the surrounding air to consider their strong coupling. The optimisation of flight performance is conducted using fluid-structure interaction analysis to achieve sufficient lift force to support the weight of an FWNAV. The design of a tethered and flyable FWNAV with a size of 10 mm or smaller is demonstrated. This FWNAV can be easily fabricated using polymer micromachining.