Different from the conventional X-ray point tube, the cold-cathode flat-panel X-ray source (FPXS) achieved planar integration of tens of thousands of X-ray point sources. However, the X-ray source distribution of the FPXS at the generating plane (Mo target) is unknown and cannot be directly measured, which hinders its practical use. To address this issue, we propose to decompose the X-ray distribution of the FPXS from the aliased projection of a coded mask. The aliased projection was a circular convolution of the source distribution of FPXS and the basic coded mask, which uniquely encodes the FPXS flux. Besides, the maximum-likelihood expectation-maximization (ML-EM) algorithm was derived to reconstruct the source distribution. Both Monte Carlo (MC) simulation and real experiments were conducted to demonstrate the effectiveness of the proposed method. In the real experiments, the X-ray emission shapes formed by placing lead plates on the surface of the anode substrate of two FPXSs were successfully reconstructed by the proposed method. Moreover, knowing and then compensating the non-uniformity distribution of the FPXS is paramount for future novel and practical applications of the X-ray source.