A noble effort, sir!
The animation appears to be wasteful of fuel.
Here’s how it would work: The lungflap opens and the firelung draws in air. Closing the lungflap and spraying fuel into the firelung, then igniting it causes an explosion as the gases expand, driving the wings downward in a power-stroke.
As the wings are raised again, the fire-lung squeezes out the exhaust gases and takes in fresh air to start the process over. It’s a two-stroke operation, with no need for oil to be added.
The dragons produce alcohol as a natural biological product from the vegetation they consume.