mmWave communication has come up as the unexplored spectrum for 5G services. With new standards for 5G NR positioning, more off-the-shelf platforms and algorithms are needed to perform indoor positioning. An object can be accurately positioned in a room either by using an angle and a delay estimate or two angle estimates or three delay estimates. We propose an algorithm to jointly estimate the angle of arrival (AoA) and angle of departure (AoD), based only on the received signal strength (RSS). We use mm-FLEX, an experimentation platform developed by IMDEA Networks Institute that can perform real-time signal processing for experimental validation of our proposed algorithm. Codebook-based beampatterns are used with a uniquely placed multi-antenna array setup to enhance the reception of multipath components and we obtain an AoA estimate per receiver thereby overcoming the line-of-sight (LoS) limitation of RSS-based localization systems. We further validate the results from measurements by emulating the setup with a simple ray-tracing approach.