Atomistic simulations have been very useful for predicting the viscoelastic properties of polymers but face great difficulties in accessing the dynamics of dense, well entangled long chain melts with relaxation times longer than mu s due to the high computational cost required. A plethora of coarse-grained models have been developed to address longer time scales. In this article we present a multiscale simulation strategy that bridges detailed molecular dynamics (MD) simulations to slip-spring based Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of long-chain polymer melts. The BD/kMC simulations are based on a mesoscopic Helmholtz energy function incorporating bonded, slip-spring, and nonbonded interaction contributions (Macromolecules 2017, S0, 3004). Bonded contributions are expressed as sums of stretching and bending potentials of mean force derived from detailed MD simulations of shorter-chain melts, while nonbonded interaction contributions in the absence of slip springs are derived from an equation of state that is consistent with thermodynamic properties predicted by detailed MD and measured experimentally. Monodisperse linear polyethylene melts of chain lengths C-260 to C-2080 are used as a test case. Estimates of the chain self-diffusivity, the longest relaxation time, the stress relaxation modulus, and the zero-shear viscosity from ms-long equilibrium BD/kMC simulations are in excellent agreement with MD results for the shorter-chain melts and with experiment. The BD/kMC scheme is extended to simulate Couette flow using Lees-Edwards periodic boundary conditions over a range of Weissenberg numbers (Wi) from 10(-2) to 10(5). Predictions for the shear viscosity as a function of shear rate, the first and second normal stress difference coefficients, the startup shear stress, as well as for changes in chain conformation and entangled structure with increasing Wi are in favorable agreement with experimental and atomistic simulation evidence.