Given the friction and drag reduction effects observed in various biological hexagonal structures in nature, a new design was implemented on the rubber surface of the stator of a submersible screw pump. This design featured a multilayer concentric hexagonal groove structure. Furthermore, a composite multilayer hexagonal structure integrating grooves and pits was also developed and applied. This study investigated the influence of groove layer number, groove depth, pit depth, and multilayer hexagonal groove texture arrangement on the rubber surface flow characteristics. Additionally, the pressure field state, the degree of influence on the oil film-bearing capacity, and the biomimetic and hydrodynamic lubrication theories were tested using the finite element analysis method. Tribological experiments were conducted on nanosecond laser-processed rubber textures under simulated liquid lubrication conditions, reflecting actual shale oil well experiments. These experiments aimed to investigate the influence of multilayer hexagonal shape parameters on the tribological characteristics of the stator-rotor friction pair of a submersible screw pump. The results indicated that with a constant overall size, a multilayer hexagonal structure with ~0.1 mm groove depth enhanced the oil film-bearing capacity, providing significant friction and drag reduction. For composite textures, a deeper pit depth within the study area enhanced the oil film-bearing capacity. Furthermore, a gradient arrangement of groove textures featuring wider outer grooves and shallower depth exhibited superior performance in terms of bearing capacity.