Different concentration malachite green oxalate (MGO) dye doped stretchable hydrogel have been prepared for synthetic circuits in flexible organic electronic devices by using the polymerization method. Frequency evolution of the tangent factor, complex impedance, phase angles, electric modulus, capacitance, and ionic conductivity for MGO dye doped hydrogel were investigated by using the impedance spectroscopy (IS) in the frequency range of 100 Hz to 40 MHz at room temperature (RT). The total polarization effects, the electric modulus-based Cole-Cole diagrams and their adopted to Smith-Chart were analyzed by the ion-migration in the hydrogel channels. The critical frequency of the imaginary part of the electric modulus increases with increasing MGO concentrations from 50 mg/L to 100 mg/L but excluding 25 mg/L. It was observed the alternative behaviour for 75 mg/L doped hydrogel originated from the fluctuation behaviour of interview interaction between MGO cationic ions and hydrogel bond. The highest and lowest values of capacitance for 25 mg/L and 75 mg/L concentrations were recorded at low frequency (LF). It was found that the conductivity properties are related to the change in the grain size of hydrogel structure because of increasing MGO concentrations.