We present a new simulation framework to estimate X-ray synchrotron fluxes from extensive air showers at high altitude. Our simulation approach builds upon analytic expressions for the spectra of synchrotron radiation found in literature, which are combined with parameterized electron population distributions and longitudinal shower profile templates to calculate the expected synchrotron emission from the EAS. After accounting for photon propagation through the atmosphere, we then estimate the resulting photon fluxes at the detection plane. For a sub-orbital detector at 36 km, it was found that for near-horizontal showers $\mathcal{O}(10^4)$ photons arrive to the detector position, distributed over an area ranging from $\mathcal{O}(10\,\text{m}^2)$ up to $\mathcal{O}(100\,\text{m}^2)$, depending on the photon energy band. These fluxes suggest that X-ray synchrotron emission is potentially a detectable signal for balloon-borne experiments.