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Flaring is a combustion process commonly used in the oil and gas industry to dispose flammable waste gases. Flare flameout occurs when these gases escape unburnt from the flare tip causing the discharge of flammable and/or toxic vapor clouds. The toxic gases released during this process have the potential to initiate safety hazards and cause serious harm to the ecosystem and human health. Flare flameout could be caused by environmental conditions, equipment failure and human error. However, to better understand the causes of flare flameout, a rigorous analysis of the behaviour of flare systems under failure conditions is required. In this article, we used fault tree analysis (FTA) and the dynamic Bayesian network (DBN) to assess the reliability of flare systems. In this study, we analysed 40 different combinations of basic events that can cause flare flameout to determine the event with the highest impact on system failure. In the quantitative analysis, we use both constant and time-dependent failure rates of system components. The results show that combining these two approaches allows for robust probabilistic reasoning on flare system reliability, which can help improving the safety and asset integrity of process facilities. The proposed DBN model constitutes a significant step to improve the safety and reliability of flare systems in the oil and gas industry.