Teshuvah:

It depends on which version of a dragon you are using. Does it eat? Is it carnivorous? Is it sentient? Many different genres of fantasy understand dragons in very different ways. While all of these are important questions, and impact the kashrut status of the organism. However, these are larger question. Classically Kashrut questions regarding new animals often look at the physical body and environment in which the organism lives.

 So: Is a dragon a land animal, a fish, a bug,  or a bird? Each of these has different signs indicating whether it is a kosher animal.

Kosher domesticated land animals have cleft hooves and chew their cud.  Is a dragon a Land animal? Even if it was, I have not read of dragons which have hooves, or chew their cud.

Kosher fish have fins and scales . So is a dragon a sea animal? That categorization is more convincing, but it depends on what version you use. You could compare it to the Leviathan, which may in fact be kosher (B Chullin 67, B. Bava Batra 75.) However the use of the term "leviathan" is not in and of itself evidence. The person might be referring to a "ghost leviathan" from Subnautica, which does not have scales. 

It is debatable whether or not bugs have signs. But even if they did, there are only a few species, all named in classical sources, that could be considered kosher. 

So that leaves birds. And considering that birds are dinosaurs, there might be something to that category.

Birds are complicated from a Kashrut perspective. The signs that indicate that they are kosher are not given in the Written Torah, only a list of birds that are kosher and some that are not. There is a huge debate about whether it is even possible to permit birds not on the list, which has somewhat been resolved, but not entirely.

So, assuming that a dragon is a bird, and assuming that it is permissible to add birds to the list of permitted animals based on the signs, a dragon would need a few specific biological characteristics. 

1. It cannot attack with its claws and eat. This can be defined in a few ways. Rambam defines it as a bird of prey (MT Forbidden Foods 1:16).  Chabad defines it as a bird that does any of the following (https://www.chabad.org/library/article_cdo/aid/3649755/jewish/What-Are-the-Signs-of-a-Kosher-Bird.htm)

   1. seizes its food with its claws and lifts it off the ground to its mouth 

   2. a bird that holds down its prey with its claws and breaks off small pieces to eat

   3. a bird that hits its prey with its feet and ingests its prey while it is still alive

   4. a bird that pounces on its prey with its claws

   5. a bird that injects a sort of venom into its prey.

2. It must also have at least one of the following:

   1. An extra claw on its feet (meaning almost an ankle spur, although you might be able to find other definitions)

   2. A crop

   3. The gizzard membrane can be peeled

In determining what a dragon might look like, perhaps te best prototypical dragon description can be found in Dungeons and Dragons. A brief overview of the section reveals the following:

Dragons do not have crops. Dragons vomit poison, acid, etc. Dragons have 4 legs. Some, not all dragons, may have the accepted 4th claw. Some, not all dragons, may be

non-carnivorous

Conclusion:

Based on the sentience, lack of a crop, lack of tradition,  difficulty in proper kosher slaughter, and other issues, I cannot recommend dragon meat as kosher.

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Originally written for https://www.reddit.com/r/Judaism/comments/1b8q8r5/comment/ktsdee1/

Sources:

https://dragons.fandom.com/wiki/Dragon_Physiology_(Dungeons_%26_Dragons)