We present a data-driven analysis of a concrete Supersymmetric (SUSY) Grand Unified Theory (GUT) of flavour, based on SU(5) × S$_{4}$, which predicts charged fermion and neutrino mass and mixing, and where the mass matrices of both the Standard Model and the Supersymmetric particles are controlled by a common symmetry at the GUT scale. This framework also predicts non-vanishing non-minimal flavour violating effects, motivating a sophisticated data-driven parameter analysis to uncover the signatures and viability of the model. This computer-intensive Markov-Chain-Monte-Carlo (MCMC) based analysis includes a large range of flavour as well as dark matter and SUSY observables, predicts distributions for a range of physical quantities which may be used to test the model. The predictions include maximally mixed sfermions, μ → eγ close to its experimental limit and successful bino-like dark matter with nearby winos (making direct detection unlikely), implying good prospects for discovering winos and gluinos at forthcoming collider runs. The results also demonstrate that the Georgi-Jarlskog mechanism does not provide a good description of the splitting of down type quark masses and charged leptons, while neutrinoless double beta decay is predicted at observable rates.