We investigate a speculative short-distance force, proposed to explain discrepancies observed between measurements of certain neutral current decays of $B$ hadrons and their Standard Model predictions. The force derives from a spontaneously broken, gauged $U(1)B3-L2$ extension to the Standard Model, where the extra quantum numbers of Standard Model fields are given by third family baryon number minus second family lepton number. The only fields beyond those of the Standard Model are three right-handed neutrinos, a gauge field associated with $U(1)B3-L2$ and a Standard Model singlet complex scalar which breaks $U(1)B3-L2$, a `flavon'. This simple model, via interactions involving a TeV scale force-carrying $Z\prime$ vector boson, can successfully explain the neutral current $B-$anomalies whilst accommodating other empirical constraints. In an ansatz for fermion mixing, a combination of up-to-date $B-$anomaly fits, LHC direct $Z\prime$ search limits and other bounds rule out the domain 0.15 TeV 1.9 TeV at the 95$\%$ confidence level. For more massive $Z\prime$s, the model possesses a {\em flavonstrahlung}
signal, where $pp$ collisions produce a $Z\prime$ and a flavon, which subsequently decays into two Higgs bosons.