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Double perovskites have attracted much interest in thermoelectric energy conversion for their ultralow thermal conductivity. Here, we report first-principles-based machine learning calculations of recently synthesized B-site columnar-ordered halide double perovskites Cs2AgB(II)X5 (B(II): Pd or Pt; X: Cl or Br) on thermal conductivities. Unlike other double perovskites, the B(II) cation in Cs2AgB(II)X5 forms a planar square with four halide anions, which breaks regular [AgX6] octahedra motions and induces strong lattice anharmonicity and thermal anisotropy. We find that thermal expansion and phonon renormalization are vital to determine the harmonic and anharmonic phonon properties of these perovskites. Furthermore, contributions from both particlelike and wavelike phonons are comprised to correctly predict the ultralow thermal conductivity as revealed by experimental measurements, and at room temperature, the thermal conductivity of Cs2AgPdBr5 along the x-direction is as low as 0.16 W/m K, which is among the lowest thermal conductivities of all-inorganic perovskites. Our study demonstrates the strong lattice anharmonicity caused by unusual atom vibrations that are distinguished from other double perovskites and facilitates the understanding of thermal transport in B-site columnar-ordered halide double perovskites.