In this study, an iterative design window (DW) search using nonlinear dynamic simulation was proposed for polymer micromachined flapping-wing nano air vehicles (FWNAVs) that can satisfy both nonlinear and unsteady design requirements, which are contradictory to each other. The DW is defined as an existing area of satisfactory solutions in the design parameter space. The present FWNAVs have a complete 2.5-dimensional structure such that they can be fabricated using polymer micromachining. The micro-wing of our FWNAVs has been designed using morphological and kinematic parameters of an actual dipteran insect. Finally, using our method, we found the DW that allowed miniaturization of the design down to 10 mm while satisfying all the design requirements. Our findings demonstrate the possibility of further miniaturizing FWNAVs down to the size of small flying insects.