We investigate the power flux relationships of guided waves in a three-layered slab waveguide with chiral metamaterial. This waveguide model contains an interfaces between adjacent layers. The graphene was used for this purpose as a result of its excellent optical properties. The interfaces thickness is 1.02nm , where three monolayer graphene were used. Power equations were obtained as well as Poynting vector for this type of structures and graphene properties. The physical explanations for such phenomenon have also been presented. Simulation results have validated our theoretical analysis. The power profiles in waveguide regions are potted and discussed. The results show unexpected characteristics including the absence of zero mode caused by the graphene interface in waveguide structure. The even modes do not provide any support for the fundamental mode for any parameters used.