This article presents the methodology and results developed as part of the Integration of Energy Resources through Local Electricity Markets (IREMEL) project, whose aim is to assess the capability of flexibility markets to manage eventual distribution network (DN) congestion produced by a high penetration of distributed energy resources (DERs), including photovoltaic (PV) panels, battery energy storage systems (BESSs), and electric vehicles (EVs). The distribution system simulator OpenDSS has been used to simulate three Spanish DNs under multiple DER penetration scenarios considering an urban and rural low-voltage network and an industrial medium-voltage DN. Likewise, the congestion events detected in the annual simulations have been used to measure the potential of flexibility markets under different DER penetrations and energy pricing. The results suggest that oversized distribution networks could prevent a profitable flexibility market implementation since the simulations developed in this article shows that networks with high congestion levels are prime candidates to solve this issue through a market mechanism. Likewise, the results suggest that a proper price for the energy managed through a local flexibility market (LFM) could have a bigger effect on market viability than DER penetration.