Understanding the mechanism of NOx formation and destruction is a prerequisite for the development of effective NOx mitigation techniques in ammonia flames. Laboratory-scale laminar ammonia (NH3) flames are well suited for such fundamental kinetic studies as the complex interaction between chemistry and fluid flow can be largely decoupled. However, quantitative and spatially resolved NO/N2O concentration data in canonical laminar ammonia flames are surprisingly scarce. Such data is, on the other hand, crucial for developing and validating kinetic models for NH3 combustion. In this regard, we developed a novel NO/N2O measurement method combining microprobe sampling and calibration-free mid-infrared laser absorption spectroscopy and realized spatially-resolved detection with high accuracy and large dynamic ratio. The fidelity of the method has been rigorously tested before being applied to perform a comprehensive parametric study on NO and N2O formation in NH3-CH4 co-fired burner-stabilized premixed flames. The effects of NH3 fuel ratio, equivalence ratio and flame temperature on NO/N2O formation have been experimentally determined. Corresponding numerical modelling was also performed using literature-based mechanisms to provide kinetic insights into the experimental observations. It is found that existing mechanisms generally have satisfactory predictions in fuel-lean flames; however, under fuel-rich conditions, these mechanisms overpredict NO formation but underestimate its destruction, leading to significant over-prediction. Such discrepancies were further investigated through sensitivity and reaction pathway analysis. The present study not only provides extensive spatially-resolved NO/N2O data in ammonia flames that are urgently needed for the development and validation of NH3 combustion mechanisms, the comparison between neat CH4 and NH3-cofired flames also points to the fact that traditional NOx mitigation techniques that are popular in combustion of hydrocarbon fuels may not be appropriate in NH3 flames. Perhaps most interestingly, the present experimental results show an oxygen-enriched oxidizer can in some cases reduce NO emission from NH3 flames.