According to my experience of learning 26 different languages, there is no universal rule in the ordering of adjectives.
As you know, there are two types of adjective usage i.e. attributive and predicative.
I guess you are only interested on attributive adjective in this question.
As you might guess, all attributive adjectives precede the noun in Korean.
We call the adjective comes before noun as 관형어(adnoun)
There are 3 types of adnoun in Korean
1. 지시관형어(demonstrative adnoun)
e.g. 이, 그, 저, 요, 이런, 저런, 그런, 다른, 무슨, 어느 (this, that, such, those, these, other, which ...)
2. 수관형어(numeral adnoun)
e.g. 한, 두, 세(석, 서), 네(넉, 너), 몇, 많은, 약간의 (one, two, a, many, much, some ..)
3. 성상관형어(descriptive adnoun)
e.g. 새, 헌, 헛, 옛, 빨간, 파란 (new, old, blue, red)
It is possible to use more than one adnominal in the same sentence, but in such circumstances Korean observes the order demonstrative adnoun - numerical adnoun - descriptive adnoun.
e.g.
이 두 젊은 남녀는 서로 사랑하는 사이입니다.(demonstrative + numeral + descriptive adnoun)
This young boy and girl love each other.
The order between descriptive adnouns is not defined.
You can follow the order of English sentence.
This is a very short, easy, and fun game.
이것은 아주 짧고 쉽고 재미있는 게임이다.
The tall kind-hearted working man was out of town.
그 키가 크고 친절한 직원은 출장중이었다.
The dirty and crowded city is so scary.
지저분하고 붐비는 도시는 너무 무섭다.
I gave her a little white stuffed animal for Christmas.
나는 그녀에게 크리스마스선물로 작고 하얀 봉제동물인형을 주었다.
"the beautiful big red ball" would be
그 아름답고 크고 빨간 공
"the big black dog" would be
그 크고 검은 개