Let’s start with that butane lighter; it does exert a force, it’s just miniscule, and unrelated to the flame. The body contains butane under pressure, so when you open the valve you allow atmospheric pressure and the lighter to equalize. Recall that each action causes an opposite reaction, and depending on the size of the valve a force pushing the body of the lighter down compared to the direction of the vale is created.
Now for the rocket, it also contains pressurized fuel (and oxidizer), but the analogy breaks down, because that’s not what causes the (bulk of the) lifting force. In the rocket engine, where fuel and oxidizer meet in a specific ratio and are ignited a huge volume of hot gas is created. Again, equal and opposite reaction, the gas wants to escape because the atmosphere has relatively lower pressure and by the shape of the exhaust it is directed downwards causing an opposite reaction on the rocket lifting it upwards.
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