Photonuclear data are increasingly used in fundamental nuclear research and technological applications. These data are generated using advanced \(\gamma\) -ray sources. The Shanghai laser electron gamma source (SLEGS) is a new laser Compton scattering \(\gamma\) -ray source at the Shanghai Synchrotron Radiation Facility. It delivers energy-tunable, quasi-monoenergetic gamma beams for high-precision photonuclear measurements. This paper presents the flat-efficiency detector (FED) array at SLEGS and its application in photoneutron cross-section measurements. Systematic uncertainties of the FED array were determined to be 3.02% through calibration with a \(^{252}\) Cf neutron source. Using \(^{197}\) Au and \(^{159}\) Tb as representative nuclei, we demonstrate the format and processing methodology for raw photoneutron data. The results validate SLEGS’ capability for high-precision photoneutron measurements.