I think Arcanine is most based off of Shisha (from the Ryukyuan culture of China). Shisha appeared as a cross between lions and dogs and were used as protection against evil spirits. Indeed, in the original Yellow Pokédex entry it says that Arcanine is considered a legendary Pokémon in China.
There is a Chinese legend that says a king had a Shisha in his necklace and visited a town that was being continuously destroyed by a sea dragon who curiously shares similarities with Gyarados. The king was beseeched to protect the town and held up his necklace before him. A deafening roar shook the earth and a giant rock appeared from heaven, crushing the dragon.
In the Yellow Pokédex, Gyarados is known to have “totally destroy[ed] cities in ancient times”.
So I believe that Arcanine was most based off of the Shisha and this particular legend in Chinese mythos.
The link I provided also mentions that some of Arcanine’s other inspirations were the Komainu (the guardian statues of Chinese shrines), the Xiezhi and Haetae, which are of Chinese and Korean origin, respectively.
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