This paper introduces a novel hybrid method using a combination of an H-infinity filter and artificial neural network (ANN) to estimate flicker components within power distribution system voltages. The H-infinity filter first extracts the estimated envelope of the applied voltage waveforms, incorporating a new voltage fluctuation model that realistically accounts for both harmonic and flicker components. Furthermore, an ADALINE (adaptive linear neuron) extracts the specific flicker components within the envelope. The hybrid process decouples prediction states, enhancing convergence behavior. Additionally, it showcases robust flicker component tracking even in the presence of power harmonics and noise, offering advantages over traditional signal processing methods. The algorithm's performance in flicker estimation is validated through statistical analysis using Monte Carlo (MC) simulations and real world data.