The network trend of isolated communities adds urgency to accelerate the deployment of community integrated energy systems (CIES). CIES effectively combines and optimizes multiple energy systems, leveraging their complementarity for efficient utilization and economical energy supply. However, the escalating intricacies of coupling multiple energy sources and the rising system uncertainties both pose challenges to flexibility scheduling of energy supply and demand. Additionally, the potential flexibility of building thermal inertia and pipeline gas linepack in diverse CIES, encompassing residential, commercial, and industrial communities, remains unexplored. To tackle these issues, a stochastic model predictive control (SMPC) based multi-temporal-spatial-scale flexibility scheduling strategy considering multiple uncertainty sources and system inertia components is proposed. First, the optimization model of CIES is formulated to improve operational flexibility and efficiency, resolve energy discrepancies and expand the capacity for renewable energy utilization. Then, the SMPC-based framework embedding an auto-regressive model and scenario generation method are established to make real-time corrections to the day-ahead scheduling stage and offset the prediction errors of uncertainty sources economically. Furthermore, thermal inertia of the aggregated buildings with different envelopes and linepack in gas pipelines are both leveraged to enhance the flexibility and synergy of CIES. Finally, a case study is executed to verify the effectiveness and applicability of the proposed strategy. The simulation results unequivocally demonstrate that this strategy successfully coordinates and harnesses complementary advantages from various energy sources, fostering a balanced energy supply-demand equilibrium across multiple temporal and spatial scales.