In this paper, the changes in exergy efficiency and exergy destruction of the process of co-production of liquefied natural gas (LNG), ethane, and the feasibility of electricity production by recovering the energy from burning flare gas and transferring it to the natural gas liquefaction unit with two cooling cycles are investigated. In order to recover the energy from the flare gas, by presenting a new process, the energy of this unit has been used to generate electricity and supply the energy required by the distillation towers in the liquefaction unit. Next, the effect of changing the feed gas flow rate on the process parameters was investigated. The exergy efficiency of the main units and the entire process was also calculated separately. The results show that with increasing feed flow rate, the exergy efficiency of the feed gas liquefaction unit increases slightly and the exergy efficiency of the flare gas recovery unit increases significantly. The exergy efficiency of the entire process also decreases by about 1.11%, which is due to the increase in the power consumption in the compressors, the decrease in power output in turbines, and the increase in the flow rates. The highest percentage of exergy destruction is related to the reactor, heat exchangers, and water coolers, respectively. Moreover, economic analysis reveals that increasing the feed gas flow rate enhances the process's Net Present Value (NPV). The results of this study showed that the proposed new process has a high potential for producing LNG.