A combination of searches for Higgs boson decays into a visible photon and a massless dark photon (H → γγd) is presented using 139 fb−1 of proton-proton collision data at a centre-of-mass energy of 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 → γγd) < 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 mH = 400 GeV to 1.0 fb (1.5 fb) for mH = 3 TeV. Results are also interpreted in the context of a minimal simplified model.