The integrated energy systems (IESs) offer a practical solution for achieving low-carbon targets in residential buildings. However, IES encounters several challenges related to increased energy consumption and costs due to fluctuations in renewable energy generation. Leveraging building flexibility to address these power fluctuations within IES is a promising strategy, which requires coordinated control between air-conditioning systems and other IES components. This study proposes a cross-time-scale control framework that contains optimal scheduling and on-the-fly flexible control to reduce the cost impacts of a residential IES system equipped with photovoltaic (PV) panels, batteries, a heat pump, and a domestic hot water tank. The method involves three key steps: solar irradiance prediction, day-ahead optimal scheduling of energy storage, and intra-day flexible control of the heat pump. The method is validated through a high-fidelity residential building model with actual weather and energy usage data in Frankfurt, Germany. Results reveal that the proposed method limits the cost increase to just 2.67% compared to the day-ahead schedule, whereas the cost could increase by 7.39% without the flexible control. Additionally, computational efficiency is enhanced by transforming the mixed-integer programming (MIP) into nonlinear programming (NLP) problem via introducing action-exclusive constraints. This approach offers valuable support for residential IES operations.