  The $B_3-L_2$ $Z^\prime$ model may explain some gross features of the fermion
mass spectrum as well as $b\rightarrow s \ell \ell$ anomalies. A TeV-scale
physical scalar field associated with gauged $U(1)_{B_3-L_2}$ spontaneous
symmetry breaking, the flavon field $\vartheta$, affects Higgs phenomenology
via mixing. In this paper, we investigate the collider phenomenology of the
flavon field. Higgs and $W$ boson mass data are used to place bounds upon
parameter space. We then examine flavonstrahlung (${Z^\prime} \rightarrow
Z^\prime \vartheta$ production) at colliders as a means to directly produce and
discover flavon particles, providing direct empirical evidence tying it to
$U(1)_{B_3-L_2}$ symmetry breaking. A 100 TeV FCC-hh or a 10 TeV muon collider
would have high sensitivity to flavonstrahlung, whereas the HL-LHC can observe
it only in extreme corners of parameter space.
