A combination of searches for Higgs boson decays into a visible photon and a massless dark photon (H -> gamma gamma(d)) is presented using 139 fb(-1) of proton-proton collision data at a centre-of-mass energy of root s = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider. The observed (expected) 95% confidence level upper limit on the Standard Model Higgs boson decay branching ratio is determined to be B(H -> gamma gamma(d)) < 1.3% (1.5)%. The search is also sensitive to higher-mass Higgs bosons decaying into the same final state. The observed (expected) 95% confidence level limit on the cross-section times branching ratio ranges from 16 fb (20 fb) for m(H) = 400 GeV to 1.0 fb (1.5 fb) for m(H) = 3 TeV. Results are also interpreted in the context of a minimal simplified model.