Let's assume that dragons show incomplete dominance for fire breathing. The F allele provides lots of fire and the F' allele gives no fire.

If a dragon that has very strong fire is crossed with a dragon that has a moderate fire, what will their offspring be like?

The progenies of the dragons with strong fire and dragon with no fire will be dragons with fire at medium rate.

Explanation:

Incomplete dominance is the phenomenon when two different alleles are present in a same organism gives a mixed type of phenotype which isn't similar to any characters of the parents.

In case of the dragons, the genotype of the dragons with strong fire = FF.

The genotype of the dragons with no fire = F'F'.

So the gametes produced by the dragon with strong fire is F and that by the dragons with no fire is F'.

So the dragons produced as a progeny = FF'.

As this gene shows incomplete dominance, so both the characters will be mixed and present as a mixed character. So the offsprings will be moderately fire breathing.