It's kind of depend on the sense of feeling as to the arrangement of adjectives in Chinese.
There is even some exceptions in the rule of adjective order in English.
換言之,語感和習慣有時會讓規則有彈性空間。
Here's some sentences I provide referring to your original descriptions in order to show you the basic guideline of adjective order in Chinese:
1) 一張新的小紅木椅
2)一張新的紅色小木椅
3)一張小的新紅色木椅
with extra information:
4)一張新的古典小紅木椅
5)一張新的古典中式小紅木椅