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In the pursuit of advanced ceramic materials with exceptional irradiation-resistance and high-temperature tolerance for nuclear applications, compositionally complex carbides (CCCs) have emerged as a highly promising class of candidate materials for extreme environments. In such conditions, critical material properties such as thermal stability, elasticity, thermal conductivity and thermodynamics behavior are predominantly influenced by phonons. In CCCs, pronounced cation disorder can lead to significant phonon scattering due to inherent mass and force constant variations, impacting these critical properties. In this study, we used ab initio calculations to predict the phonon band structures and systematically explore the influence of mass and force constant variance on the phonon spectral function of CCCs with a rock salt structure, ranging from binary to five-metal component carbides. Our findings reveal that the selection and concentration of constituent elements can be strategically utilized to tune the phonon band structure, phonon bandgap and phonon scattering in CCCs, thereby enabling control over phonon-related properties. Additionally, we measured the thermal conductivity of some of these CCCs using the spatial-domain thermoreflectance technique. Interestingly, the measured thermal conductivity of some of these CCCs indicates that five-component ceramics exhibit higher thermal conductivity than certain ternary and binary alloys. This observation contrasts with the expectation that greater cation disorder would result in more scattering and lower thermal conductivity. This intriguing result opens up the possibility of discovering CCCs with better thermal conductivity, presenting new opportunities for their application in extreme environments.