Electron spin states of solid-state defects such as Nitrogen- and Silicon-vacancy {\em color centers} in diamond are a leading quantum-memory candidate for quantum communications and computing. Via open-quantum-systems modeling of spin-phonon coupling -- the major contributor of decoherence -- at a given temperature, we derive the time dynamics of the density operator of an electron-spin qubit. We use our model to corroborate experimentally-measured decoherence rates. We further derive the temporal decay of distillable entanglement in spin-spin entangled states heralded via photonic Bell-state measurements. Extensions of our model to include other decoherence mechanisms, e.g., undesired hyperfine couplings to the neighboring nuclear-spin environment, will pave the way to a rigorous predictive model for engineering artificial-atom qubits with desirable properties.