We employ advanced first-principles methodology, merging self-consistent phonon theory and the Boltzmann transport equation, to comprehensively explore the thermal transport and thermoelectric properties of KCdAs. Notably, the study accounts for the impact of quartic anharmonicity on phonon group velocities in the pursuit of lattice thermal conductivity and investigates 3ph and 4ph scattering processes on phonon lifetimes. Through various methodologies, including examining atomic vibrational modes and analyzing 3ph and 4ph scattering processes, the paper unveils microphysical mechanisms contributing to the low $\kappa_{L}$ within KCdAs. Key features include significant anisotropy in Cd atoms, pronounced anharmonicity in K atoms, and relative vibrations in non-equivalent As atomic layers. Cd atoms, situated between As layers, exhibit rattling modes and strong lattice anharmonicity, contributing to the observed low $\kappa_{L}$. Remarkably flat bands near the valence band maximum translate into high PF, aligning with ultra-low $\kappa_{L}$ for exceptional thermoelectric performance. Under optimal temperature and carrier concentration doping, outstanding \textit{ZT} values are achieved: 4.25 (a(b)-axis, p-type), 0.90 (c-axis, p-type), 1.78 (a(b)-axis, n-type), and 2.36 (c-axis, n-type).