I am not going to address the Chinese long, since I don't know enough about it, but it is a chimeric creature that is not obviously similar to legendary serpentine creatures. For the rest, it is best to forget a moment about the winged-and-fire-breathing creature we call a dragon, and instead think about serpents. The chaoskampf motif, where a hero or deity slays a primordial serpent, typically associated with water, is present in one way or another in an astonishing range of mythologies, off the top of my head:

• Thor and Jörmungandr

• Zeus and Typhon, Herakles and the Hydra

• Indra and Vritra (Vedic)

• Thraetaona and Azi Dahaka (Zoroastrian)

• Tarhunz and Illuyanka (Hittite)

• Yahweh and Leviathan¨

• Ba'al and Lotan (Ugaritic)

• Susano'o and Orochi (Japanese)

• Marduk and Tiamat (Babylonian) [though whether Tiamat can really be called a "serpent" has been disputed]

(There are more for sure.)

The question is whether these have a common origin, and I would say that it is likely that they do. Norse, Greek, Vedic, Zoroastrian, and Hittite can all be explained through a common Indo-European origin - these mythologies have a general common ancestor. It is plausible that the story could have made its way to Japan by the time it is attested, in the ~7th century AD, by way of Buddhist monks. This leaves us wondering whether it originated in the Near East or with the Proto-Indo-Europeans who dwelled in the Eurasian steppes, and the only plausible explanation I can see is that it originated with the Indo-Europeans.

This is for the simple reason that the interaction between the non-Anatolian Proto-Indo-Europeans and the Near East was very limited and several steps removed (the Caucasus being in the way). On the other hand, the timeframe makes it plausible, even likely, that the Anatolian peoples like the Hittites could have transmitted the myth to Near Eastern civilizations. When exactly the Marduk and Tiamat myth dates to is a bit unclear, but the Anatolian languages split off from the other Indo-European ones sometime in the 4th milennium BC, which is certainly early enough to have transmitted it.

This is generally about as far as you will get with comparative mythology. One may always quibble with the details of any one of the legend and question whether they are similar enough to really suggest a common ancestor, though in my view, there is enough similarity between the Near Eastern and Indo-European myths to warrant the supposition - particularly the hero/deity is usually associated with storms and the serpent usually with water. This is too similar to be a mere coincidence. The wide spread of the legend simply mirrors the wide spread of Indo-European cultures.

How the serpent motif evolved into the more familiar, fire-breathing dragon motif is unfortunately a bit outside my timeframe - it is a Middle Ages development that I'm not familiar with in detail. But I hope this was still interesting to you!

For the details of Proto-Indo-European interactions and migrations, I used The Horse, the Wheel and Language.

Looks like this exact question is new, so I hope you'll get some novel answers. But in the meantime, we have a section of our FAQ that has a few questions about dragons, including whether the Chinese or Europeans first invented them.

u/lcnielsen why is the identification with Tiamat as a dragon disputed?