Here we introduce gamesh, a novel pipeline that implements self-consistent radiative and chemical feedback in a computational model of galaxy formation. By combining the cosmological chemical-evolution model gamete with the radiative transfer code crash, gamesh can post-process realistic outputs of a N-body simulation describing the red-shift evolution of the forming galaxy. After introducing the gamesh implementation and its features, we apply the code to a low-resolution N-body simulation of the formation of the Milky Way and we investigate the combined effects of self-consistent radiative and chemical feedback. Many physical properties, which can be directly compared with observations in the Galaxy and its surrounding satellites, are predicted by the code along with the merger-tree assembly. The resulting red-shift evolution for the Local Group of star-formation rates, reionization and metal enrichment along with the predicted metallicity distribution function of halo stars are critically compared with observations. We discuss the merits and limitations of the first release of gamesh, which also opens new directions to a full implementation of feedback processes in galaxy-formation models by combining semi-analytic and numerical methods.