In this work, we study the interfacial boundary conditions at the interface between two immiscible liquids under a laminar flow. We measure the hydrodynamic drainage forces acting on a colloid probe as it approaches a flat and smooth Teflon film coated with silicone oil films, submerged in a sucrose solution using atomic force microscopy. On Teflon substrates, silicone oil films of thickness several hundred nanometers could be stabilized, and we found the effective slip length over these to be of the order of several hundred nanometers which increases with increasing silicone oil film thickness, as expected. The fitted slip length values weakly increased with increasing shear rates. The high values of effective slip length indicate that lubricant-infused surfaces are likely to reduce drag on length scales that approach the macroscopic scales.