  We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a
discrete $A_4$ family symmetry combined with a discrete flavour symmetry $
\mathbb{Z}_3 \times \mathbb{Z}_5^2 $, in a realistic Pati-Salam unified theory
of flavour. Imposing only these discrete flavour symmetries, the axion solution
to the strong $ CP $ problem is protected from PQ-breaking operators to the
required degree. A QCD axion arises from a linear combination of $ A_4 $
triplet flavons, which are also responsible for fermion flavour structures due
to their vacuum alignments. We find that the requirement of an accidental PQ
symmetry arising from a discrete flavour symmetry constrains the form of the
Yukawa matrices, providing a link between flavour and the strong $ CP $
problem. Our model predicts specific flavour-violating couplings of the
flavourful axion and thus puts a strong limit on the axion scale from kaon
decays.
