  We investigate the phenomenology of a non-thermal dark matter (DM) candidate
in the context of flavor models that explain the hierarchy in the masses and
mixings of quarks and leptons via the Froggatt-Nielsen (FN) mechanism. A
flavor-dependent $U(1)_{\rm FN}$ symmetry explains the fermion mass and mixing
hierarchy, and also provides a mechanism for suppressed interactions of the DM,
assumed to be a Majorana fermion, with the Standard Model (SM) particles,
resulting in its FIMP (feebly interacting massive particle) character. Such
feeble interactions are mediated by a flavon field through higher dimensional
operators governed by the $U(1)_{\rm FN}$ charges. We point out a natural
stabilizing mechanism for the DM within this framework with the choice of
half-integer $U(1)_{\rm FN}$ charge $n$ for the DM fermion, along with integer
charges for the SM fermions and the flavon field. In this flavon portal
scenario, the DM is non-thermally produced from the decay of the flavon in the
early universe which becomes a relic through the freeze-in mechanism. We
explore the allowed parameter space for this DM candidate from relic abundance
by solving the relevant Boltzmann equations. We find that reproducing the
correct relic density requires the DM mass to be in the range $(100-300)$ keV
for $n=7.5$ and $(3-10)$ MeV for $n=8.5$ where $n$ is the $U(1)_{\rm FN}$
charge of the DM fermion.
