We present three-dimensional local hydrodynamic simulations of flows around objects embedded within stellar envelopes using a "wind tunnel" formalism. Our simulations model the common envelope dynamical inspiral phase in binary star systems in terms of dimensionless flow characteristics. We present suites of simulations that study the effects of varying the binary mass ratio, stellar structure, equation of state, relative Mach number of the object's motion through the gas, and density gradients across the gravitational focusing scale. For each model, we measure coefficients of accretion and drag experienced by the embedded object. These coefficients regulate the coupled evolution of the object's masses and orbital tightening during the dynamical inspiral phase of the common envelope. We extrapolate our simulation results to accreting black holes with masses comparable to that of the population of LIGO black holes. We demonstrate that the mass and spin accrued by these black holes per unit orbital tightening are directly related to the ratio of accretion to drag coefficients. We thus infer that the mass and dimensionless spin of initially nonrotating black holes change by of order 1% and 0.05, respectively, in a typical example scenario. Our prediction that the masses and spins of black holes remain largely unmodified by a common envelope phase aids in the interpretation of the properties of the growing observed population of merging binary black holes. Even if these black holes passed through a common envelope phase during their assembly, features of mass and spin imparted by previous evolutionary epochs should be preserved.