To address the uncertainty of distributed renewable energy (RE), real-time and efficient operation of the local energy market (LEM) at the distribution level is imperative. Traditional security-constrained economic dispatch methods prove inefficient and incompatible with the high-frequency operational needs of LEM in the presence of large-scale prosumers. This study proposes an optimal operation mechanism based on the sequential clearing of energy and flexibility markets, where energy trading and congestion management are decoupled. Prosumers are offered two bidding modes to cater to their trading needs under different risk preferences. The Guaranteed Price Mode (GPM) provides a secure and predictable trading environment, while the Energy Resale Mode (ERM) allows prosumers to capitalize on market fluctuations. A continuous double auction method is proposed to clear the LEM. Dynamic calculation of power loss and network fees is implemented to incentivize prosumer trading within neighborhoods. Furthermore, a flexibility market for congestion management is established to encourage the active exploration of prosumers’ flexibility and to provide services to the distribution network. Case studies demonstrate the effectiveness of the proposed mechanism in enhancing transaction efficiency and ensuring the operational security of distribution networks.