Constitutive modelling of granular flows remains challenging due to their strong history-dependence and complex transient rheology. In poly-disperse systems, this challenge is compounded by the introduction of competing transport mechanisms. While segregation is continuously countered by diffusive remixing, bulk advection carries various particle species at different rates. Local rheology is therefore dramatically affected by the ensuing rheology-segregation coupling. Most continuum models treat these processes in isolation or rely on steady-state closures, limiting their ability to capture transient, coupled dynamics. Moreover, current continuum models are restricted to specific ranges of inertia numbers, and break down at their limits. We develop a physics- and thermodynamics-informed machine-learning framework to uncover constitutive laws governing transient segregating granular flows. High-fidelity datasets are generated through discrete element simulations of bi-disperse inclined gravity-driven chute flows and continuum fields for state and internal variable measures are obtained through coarse-graining. Carefully designed neural networks with internal variable information, learn for the first time, closure relations for rheology, granular temperature evolution, and segregation dynamics across a range of inertia numbers. Symbolic distillation extracts interpretable, reduced-order equations that reveal the dominant mechanisms driving the dynamics. Together, this framework enables accurate prediction of constitutive laws governing segregating granular flows while furnishing insights into the otherwise elusive coupled process. This approach naturally paves the way for uncovering rheological laws for a wider class of complex granular flows without relying on any phenomenological assumptions.