Atomic layer deposition (ALD) and molecular layer deposition (MLD) techniques with atomic level control enable a new class of hybrid organic-inorganic materials with improved functionality. In this work, the cross-plane thermal conductivity and volumetric heat capacity of three types of hybrid organic-inorganic zincone thin films enabled by MLD processes and alternate ALD-MLD processes were measured using the frequency-dependent time-domain thermoreflectance method. We revealed the critical role of backbone flexibility in the structural morphology and thermal conductivity of MLD zincone thin films by comparing the thermal conductivity of MLD zincone films with an aliphatic backbone to that with aromatic backbone. Much lower thermal conductivity values were obtained in ALD/MLD-enabled hybrid organic-inorganic zincone thin films compared to that of the ALD-enabled W/Al2O3 nanolaminates reported by Costescu et al. [Science 2004, 303, 989-990], which suggests that the dramatic material difference between organic and inorganic materials may provide a route for producing materials with ultralow thermal conductivity.