A high proportion of renewable energy access makes the net load of the power system volatile and uncertain, increasing the demand for the ramping capacity of the power system. Traditional electricity spot markets compensate for the power imbalances caused by an insufficient ramping capacity through traditional flexibility services such as ancillary services and interconnection power. However, conventional flexibility services may lead to frequency deviations in the power system, increased response costs, spikes in electricity prices, and dramatic price volatility in the traditional spot market. To solve the above problems, this paper proposes an FRP and convex electricity spot market joint clearing (FCESMJC) market mechanism. The FCESMJC model can more accurately represent the relationship between electrical power output and the price of electricity and reduces the number of spikes in electricity prices. In addition, a novel FRP pricing method is proposed to compensate FRP market participants for their FRP costs more reasonably. Additionally, the difference in system performance is provided by comparing the energy prices, pricing method, clearing prices, and system costs in the FCESMJC method and the traditional electricity spot market. The FCESMJC system reduces the total system cost by 18.6% compared with the electricity spot market. Numerical experiments are simulated on the IEEE 14-bus test system to validate the superiority of the proposed model.