  We investigate flavour bounds on the $\mathcal{Z}_2 \times \mathcal{Z}_5$ and
$\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetries. These flavour
symmetries are a minimal and a non-minimal forms of the $\mathcal{Z}_2 \times
\mathcal{Z}_N$ flavour symmetry, that can provide a simple set-up for the
Froggatt-Nielsen mechanism. The $\mathcal{Z}_2 \times \mathcal{Z}_5$ and
$\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetries are capable of
explaining the fermionic masses and mixing pattern of the standard model
including that of the neutrinos. The bounds on the parameter space of the
flavon field of the $\mathcal{Z}_2 \times \mathcal{Z}_5$ and $\mathcal{Z}_2
\times \mathcal{Z}_9$ flavour symmetries are derived using the current quark
and lepton flavour physics data and future projected sensitivities of quark and
lepton flavour effects. The strongest bounds on the flavon of the
$\mathcal{Z}_2 \times \mathcal{Z}_5$ symmetry come from the $D^0 - \bar D^0$
mixing. The bounds on the $\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetry
are stronger than that of the minimal $\mathcal{Z}_2 \times \mathcal{Z}_5$
symmetry. The ratio $R_{\mu \mu}$ provides rather robust bounds on the flavon
parameters in the future phase-\rom{1} and phase-\rom{2} of the LHCb by leaving
only a very small region in the allowed parameter space of the models.
