This study explores how sector coupling via Integrated energy systems (IES) can improve the operational flexibility of the power grid, while hydrogen is gaining traction as a versatile energy carrier. Specifically, we have evaluated the operational benefits of integrating two electrolytic processes for hydrogen generation, namely low-temperature electrolysis (LTE) and high-temperature steam electrolysis (HTSE), into a nuclear- renewable IES using a 3-cycle power system operation framework. Detailed steady-state models of the electrolytic hydrogen generating facilities are constructed, with the HTSE process represented using standard transient models to account for the steam-bypass scheme from the nuclear reactor. These models are then integrated into a renewable-intensive power network model (specifically, the NREL 118-bus system). To simulate the operation of the integrated system across multiple timescales, a multi-timescale scheduling and dispatch tool is employed. Results indicate that while both electrolytic processes contribute to significant flexibility enhancement and renewable energy curtailment reduction (3 MWh and 16 MWh), the LTE process offers more operational benefits than the HTSE process across multiple timescales.