The increasing penetration of renewable energy sources will impose even more stress on the operational flexibility at multiple timescales. Energy storage (ES) is a promising option to provide multiple services, while various energy storage systems (ESSs) exhibit diverse economic performances at different timescales. However, efficiently and economically combining multi-timescale ESSs to meet flexibility requirements is challenging due to the gap between coarse-grained ESS representations and multi-timescale flexibility requirements. This paper presents a wavelet packet decomposition (WPD) based multi-timescale operational flexibility quantification method. Such requirements are clustered and then satisfied by an ES planning model covering multiple timescales from intra-hourly to seasonal using representative scenarios, while considering both short-term (operational) and long-term (technology cost) uncertainties. An empirical analysis of a provincial power grid in East China is performed to obtain the planning results in 2030 and 2060. Numerical results demonstrate the effectiveness of the multi-timescale ES planning model as well as its computational performance and economic advantages.