The polymeric gel electrolytes are attractive owing to their higher ionic conductivities than those of dry polymer electrolytes and lowered water activity for enlarged potential window. However, the ionic conductivity and mechanical strength of the Na‐ion conducting polymeric gel electrolytes are limited by below 20 mS cm−1 and 2.2 MPa. Herein, we demonstrate Na‐ion conducting and flexible polymeric hydrogel electrolytes of the chemically coupled poly(diallyldimethylammonium chloride)‐dextrin‐N,N′‐methylene‐bis‐acrylamide film immersed in NaClO4 solution (ex‐DDA‐Dex + NaClO4) for flexible sodium‐ion hybrid capacitors (f‐NIHC). In particular, the anion exchange reaction and synergistic interaction of ex‐DDA‐Dex with the optimum ClO4− enable to greatly improve the ionic conductivity up to 27.63 mS cm−1 at 25°C and electrochemical stability window up to 2.6 V, whereas the double networking structure leads to achieve both the mechanical strength (7.48 MPa) and softness of hydrogel electrolytes. Therefore, the f‐NIHCs with the ex‐DDA‐Dex + NaClO4 achieved high specific and high‐rate capacities of 192.04 F g−1 at 500 mA g−1 and 116.06 F g−1 at 10 000 mA g−1, respectively, delivering a large energy density of 120.03 W h kg−1 at 906 W kg−1 and long cyclability of 70% over 500 cycles as well as demonstrating functional operation under mechanical stresses.