Accurate measurement of flash X-ray energy spectra plays an important role in highenergy flash radiography. In this paper, by virtue of Geant4 toolkit, we simulated the generation and transport of X-ray photons resulting from the interaction of a high-energy electron beam with a solid thin target. We obtained the flash X-ray energy spectral distribution in the plane perpendicular to the electron beam incident direction. Our results indicate that the flash Xray spectrum is almost uniform in the azimuthal direction but is quite different in the radius direction. Specifically, as the radius increases, the incident X-ray dose decreases significantly. Our work paves a theoretical basis for selecting appropriate structures and layout of the spectrometer and facilitates the measurements of flash X-ray energy spectra.