We present Infinite Flow Cosmology (IFC), a brane-world framework in which the observable universe is modelled as an open thermodynamic system embedded within a dynamic, radiating 5D Vaidya-Anti-de Sitter bulk spacetime. Rather than invoking a static cosmological constant, IFC drives late-time cosmic acceleration through continuous mass-energy flux projected from the bulk onto the 4D brane. Using the Shiromizu-Maeda-Sasaki projection formalism, we derive the modified Friedmann equations and a generalised energy conservation law governing bulk-brane exchange. We constrain the dimensionless bulk-brane coupling constant to α ≈ 2.2 by matching the observed late-time expansion history, and derive an effective quintessence-like equation of state w(z) ≳ −1 that is distinct from and testable against a pure cosmological constant. The model predicts a mild but measurable enhancement in the large-scale structure growth parameter fσu2088 at redshifts z < 0.5, forecasting a signal detectable by the Euclid satellite and DESI survey. Finally, we demonstrate that localised bulk flux preferentially couples to regions of extreme spacetime curvature, providing a two-channel gravity-based mechanism for super-Eddington black hole accretion that simultaneously explains anomalous mass growth rates and the persistence of bright X-ray coronae and radio jets — observations that challenge standard slim disk models