Phase-change materials (PCMs) are widely used in energy storage and thermal management due to the large latent heat in the phase-change process. As one of the most significantly thermophysical properties of PCMs, the thermal conductivity has been extensively studied. Great attention has been paid to improving the thermal conductivities of PCMs; however, the studies on the thermal conductivities of flexible PCMs are relatively inadequate. In this study, polyethylene glycol 1500 (PEG1500) was used as the base PCM, and expanded graphite (EG) and styrene–butadiene–styrene (SBS) were added to improve the thermal conductivity and flexibility of pure PCMs, respectively. A steady-state experimental test rig was built and verified with the measurement of the thermal conductivity of stainless steel and deionized water, and then the thermal conductivities of PCMs at different phases and qualitative temperatures were measured extensively. Compared to the PEG1500 with 5 wt.% EG, the addition of SBS sharply reduces the thermal conductivity, which is only 0.362 W/(m·K) at 12.5 °C when the addition ratio is 50%. This is approximately a 69% reduction compared with the composite PCMs without SBS. Furthermore, the theoretical thermal conductivities of the composite PCMs were calculated with six theoretical models of multiphase systems. The majority of the models provide a good prediction of thermal conductivities of composite PCM with high SBS concentration, while the average deviation of Agari-Uno model is only 20.5% with different SBS concentration and relatively agrees well with the experimental results.