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Increasing the penetration rate of microgrids (MGs) for Local Energy Market (LEM) participation creates new challenges for the market-clearing process under a large number of requests for energy transactions. The market-clearing process for decentralized market frameworks is dependent on participants’ flexibility in negotiations for bilateral energy transactions. Multi-energy microgrids (MEMGs) include combined heat and power units which can be less dependent on electricity prices because of energy conversion equipment, gas infrastructure, and combined heat and power loads. In this regard, to evaluate prosumers’ flexibility role in market negotiations, a new analysis based on energy scheduling of MEMG considering a Demand-Response Program (DRP) model is executed under a distributed market structure. Moreover, two new flexibility indexes for market participants with attention to prosumers’ adaption capabilities are proposed. The results show that, under a 9.35% flexibility index improvement for the entire system, the social welfare function improved by 2.75%. Moreover, the results show that the DRP model for changeable and shiftable loads can improve the flexibility of the entire system by 35.82%. Combined heat and power load are considered as the resource of flexibility for system evaluations.