  If dark photons are massless, they couple to standard-model particles only
via higher dimensional operators, while the kinetic mixing with photons, which
motivates most of the current experimental searches, is absent. We consider the
effect of possible flavor-changing magnetic-dipole couplings of massless dark
photons in kaon physics. In particular, we study the branching ratio for the
process $K^+\rightarrow \pi^+\pi^0 \bar \gamma$ with a simplified-model
approach, assuming the chiral quark model to evaluate the hadronic matrix
element. Possible effects in the $K^0$-$\bar K^0$ mixing are taken into
account. We find that branching ratios up to $O(10^{-7})$ are
allowed---depending on the dark-sector masses and couplings. Such large
branching ratios for $K^+\rightarrow \pi^+\pi^0 \bar \gamma$ could be of
interest for experiments dedicated to rare $K^+$ decays like NA62 at CERN,
where $\bar \gamma$ can be detected as a massless invisible system.
