This isn't that outlandish. There are already examples of folks who consumed some form of brewer's yeast that can get drunk when eating carbs. The yeast colonizes their GI tract and converts the sugars to alcohol, which is then absorbed into the blood stream.
A proposed system would probably require a dedicated "fermenting sac" lined with cells that actively pull away alcohol and dump it into another sac lined with acellular material or cells that are either very resistant to alcohol or secrete a film that is (think of how the gallbladder collects and concentrates bile produced by the liver). This would keep the alcohol level in the fermenting sac low enough to not kill off the fermenting organisms and concentrate enough alcohol in the storage sac to be flammable. Of course it is very difficult to biologically drive a gradient like this (pulling from a low concentration to a high one) so this will be a high energy consuming process. The dragon would need a robust alcohol degradation pathway in the liver to deal with any alcohol that got into the blood stream as there would inevitably be at least some leakage.
The alcohol could be stored in a non-flexible space (i.e. lined with corrosion resistant enamel, dense keratin [horn], chitin, or something) but it would need to be transferred into a muscle lined space in order to be propelled out (like how your stomach can contract to vomit), the space would need to be collapsible (like an accordion), it will have to be "flung" out via mechanical motion, or dispersed into the airway and moved out via exhaled air. But this would probably cause the dragon to inhale alcohol rich fumes unless it has a dedicated "blowhole" like an aquatic mammal for just this purpose.
Igniting the alcohol would be difficult via a pure biological process but perhaps the dragon could have an organ that is purposefully loaded with flint and steel (somewhat analogous to birds eating rocks to aid in mechanical digestion, i.e. the dragon ejects the alcohol from it's mouth and strikes teeth together that have embedded minerals that create a spark). Or it could have something that ignites upon exposure to air like a more volatile alcohol/gas mixture or elements like Lithium (which are horribly toxic in their own right but could be maintained in much lower quantities).
But the volume of alcohol to provide a useful stream of fire would be pretty large, severely limiting the number of times a dragon can breathe and refill the reservoir. A more payload efficient effect would be to create a aerosol cloud that is then ignited like a thermobaric fuel/air explosive but this isn't what is usually depicted in media.