Significance Molecular electrolytes under confinement are crucial materials for energy storage devices and commonly used model systems for understanding biomolecular functions. In particular, understanding the complex interplay of entropy and electrostatic interactions in a polyelectrolyte solution confined inside oppositely charged surfaces gives us important insights into its energy storage and capacitance properties. Here, using molecular dynamics simulations, we analyze polyelectrolyte solutions confined between two oppositely charged planar surfaces with a much lower dielectric constant. We find that such mismatch of dielectric constants and chain flexibility significantly influence the energy storage capability and capacitance of such a confined system. Dielectric mismatch enhances surface charge amplification in flexible polyelectrolyte solutions, increasing their energy storage capabilities.