We investigate the role of molecular flexibility on the electrical transport properties of model electrolytes containing ions and an underlying disordered network structure with changing connectedness. Rather than focusing on the effect of ion content in a stoichiometric network former AY_{2} (e.g., SiS_{2}), we explore the possibility of increasing the Y∶A ratio (flexibility index m) in order to reduce connectivity and to promote the occurrence of flexible modes and topological degrees of freedom in the network structure. At fixed ion content and below a certain threshold modifier composition x_{c}, topological constraint counting indicates that a mean-field stress-to-flexible transition is expected for a flexibility index m_{c}, and an ion hopping model predicts a substantial increase of conductivity once m>
m_{c}. Molecular dynamics simulations on a typical amorphous electrolyte, xNa_{2}S-(1-x)SiS_{m}, independently and quantitatively confirm the prediction as anomalous changes with m are obtained, and these manifest by waterlike diffusivity anomalies, and a substantial increase of ionic conductivity upon moderate change of m. The analysis disentangles contributions from mobility and the free carrier rate in the electrical transport, and finally suggests that molecular flexibility can serve as an efficient way for conductivity enhancement in all solid-state batteries using amorphous electrolytes.