Your idea is a good one, and definitely possible.
An alternative explanation might be that "dragon-fire" actually means "courage" or "bravery" (both of which are uncountable nouns). There are a couple of reasons why I think this might be a good explanation.
First, "work up the courage (to do something)" is a relatively strong collocation or chunk of language. (Though we would not say "work up the bravery".) And second, for some reason English speakers tend to think of courage as being found either in the heart or in the stomach. So, the reference to "bellies" makes me feel this is related to courage.
As to why the writer uses the phrase "dragon-fire" as opposed to "courage" or even just "fire", this is a fantasy story, it seems, and dragons are common in fantasy stories, so perhaps it sounded like a nice phrase to him or her.
I hope this helps.
Student or Learner