With the rising penetration of new energy, uncertainties on both generation and load sides pose significant risks to power system stability. To scientifically assess the flexibility of a novel multi-source coupled power system (integrating wind, solar, thermal, hydro and energy storage), a collaborative analysis framework is proposed, combining interval estimation of bilateral generation-load uncertainties with stochastic production simulation. First, non-parametric kernel density estimation generates confidence intervals for new energy output and load, and extreme supply-demand scenarios are constructed to quantify such uncertainties. Second, via a hierarchical dispatching strategy, wind, photovoltaic and run-of-river hydropower are prioritized as equivalent negative loads. Considering system ramping constraints, an improved stochastic production simulation algorithm schedules thermal power unit output. Finally, reservoir-type hydropower undertakes remaining system load. In case of load shedding or new energy curtailment, energy storage devices regulate the system through charging and discharging. Case studies show non-parametric estimation effectively characterizes bilateral generation-load uncertainties. The proportions of load shedding and new energy curtailment due to insufficient system ramping capacity are 14.8% and 91.5%, respectively, indicating ramping constraints are critical to system stability. Energy storage configuration significantly enhances regulation capacity, reducing the loss of load probability (LOLP) and new energy curtailment probability by 8.6% and 34.1%, respectively.