The LambdaCDM model confronts two increasingly significant observational conflicts: the Hubble constant H0 tension (+8.3%, >5 sigma) and the S8 tension (-8.4%, ~3 sigma). The near-identical absolute magnitudes and opposite signs of these deviations suggest a common kinematic origin rather than modifications to the cosmic energy budget. We propose a phenomenological framework in which physical proper time tau is an emergent order parameter of energy flux from higher dimensions into the 3-dimensional observable space, satisfying d tau = a(t)^{-1} d t. This yields a proper-time rate gamma(z) = d tau/dt = 1+z. Introducing a single empirical parameter Q calibrated by the observed H0 tension, the model yields an effective late-time factor gamma_late ≃ 1.083, from which the S8 tension and f sigma8 suppression follow with no additional free parameters, driven by a dynamical competition between the constant thrust from Q and the standard LambdaCDM Hubble drag. The same time-flow mechanism naturally suppresses the growth of cosmic structure, giving S8_obs ≃ 0.772, in excellent agreement with weak lensing measurements. The Friedmann equations retain their standard geometric form; the acceleration driver is the injected free-energy flux rho_de rather than an ad hoc cosmological constant. The model distinguishes between instantaneous and cumulative cosmological observables, with time-dilation measurements remaining unchanged while integrated quantities such as H0, S8 and f sigma8 exhibit the observed ~8% shifts.