This study proposes a hybrid deep-learning model that combines Convolutional Neural Networks (CNNs) with a Transformer Encoder to investigate the nonlinear dynamics of a laminar, partially premixed counterflow flame under acoustic excitation. The model was trained on experimental data obtained from a combustion instability laboratory. OH* chemiluminescence was employed to measure flame responses across a frequency range of 20 to 350 Hz and pressure amplitudes extending up to the extinction threshold. The research explores the intricate interactions between acoustic waves and flame dynamics, providing insights into how varying amplitudes and frequencies influence heat release rates. Despite inherent limitations in the dataset, the model demonstrated a robust ability to accurately approximate the flame transfer function, successfully replicating chemiluminescence signals and forecasting flame reactions to diverse acoustic excitations. Additionally, the repeatability of the flame structure was rigorously validated through high-speed imaging and image processing techniques, confirming consistent flame characteristics over multiple testing cycles. The results underline the significant promise of the hybrid deep-learning approach as a reliable tool for predicting flame behavior in complex acoustic environments, offering practical implications for mitigating combustion instabilities in various engineering applications. This research represents a significant step forward in applying machine learning techniques to enhance the predictability and control of flame dynamics in real-world systems.