The high penetration of distributed generators (DGs) and the large-scale charging loads deteriorate the operational status of flexible distribution networks (FDNs). A soft open point (SOP) can deal with operational issues, such as voltage violations and the high electricity purchasing cost of charging stations. However, the absence of accurate parameters poses challenges to model-based methods. This paper proposes a data-driven operation method of FDNs with charging loads. First, a data-driven model-free adaptive predictive control (MFAPC) approach is proposed to fully involve charging loads in the control of FDN without accurate network parameters. Then, a multi-timescale coordination control model of an SOP with charging loads is established to satisfy the demand of charging loads and improve the control performance. The effectiveness of the proposed method is numerically demonstrated on the modified IEEE 33-node distribution network. The results indicate that the proposed method can effectively reduce the electricity purchasing cost of charging stations and improve the operational performance of FDNs.