The legend of the Chinese dragon I found a story about the origin of the Chinese dragon in English but can't find it anywhere in Chinese.

The characters' names are Chi Yu and Hieun Tse in the English version.

Does anyone know if this story exists in Chinese or was it created by an English speaker?
The accepted answer is simply wrong.

It is probably from a Chinese folk tale since it claims to be Chinese. I daresay I have read similar folktales, especially the swallow-the-bead-and-turn-into-a-dragon part, when I was a kid. I cannot figure out the exact one. But it is easy to search out folk stories with similar motifs.

e.g. https://book.douban.com/subject/11633147/


  一个叫阿宝的孩子拾到了一颗红色的宝珠，他把宝珠放进米缸，米缸里立刻盛满了白花花的大米；他把宝珠放进钱罐，钱罐里立刻填满金灿灿的钱币。阿宝用这颗宝珠帮助周围的邻居都过上了好日子。奇怪的是，自从阿宝捡到这颗宝珠后，天上就再也没有下过一滴雨，大地干涸、庄稼干枯，乡亲们愁眉不展。
  
  一天晚上，阿宝在梦中见到一条雨龙在空中喷雨，醒来后，他决定动身去寻找这条雨龙。一路上，阿宝帮助了巨蛇、梅花鹿、鲤鱼和苍鹰，每个动物朋友都赠送了他一样礼物，并警告他要当心一个叫红鬼的妖怪。随后，阿宝果然遇到了红鬼，并从红鬼口中知道了自己手中的珠子叫龙珠。为了保护龙珠，找到雨龙，阿宝果断决绝地吞下了珠子。最后，在动物朋友们赠送的礼物的帮助下，阿宝变成了一条会下雨的龙，把甘露洒向了人间。


沙县民间故事
This story lacks the part of the magical power of the dragon bead, but retains the part of swallowing the bead to become the dragon.

https://www.sohu.com/a/349852173_488223

This one is rather long, but the story is almost the same, which is easy to find if you can read Chinese. 

A further question is whether this kind of folktale has a origin in Classical Chinese literature.

And I must say many Chinese folk tales have a style and sentiment that you won't find in classical Chinese literature. Not to say even China proper is a country that comprises several distinct territories, varied cultures, and peoples. It is always hard to say what is really "un-Chinese".