It's a quote from a material of an online English school. https://eikaiwa.weblio.jp/information/speaking-material/conversation-material/expert-literature-and-art
"It’s one of the greatest American literature."
The word, litarature, is uncountable, isn't it? This sentence sounds very awkward to me. I believe it should be "one of the greatest American litarature classics" or something like that.
Is this material grammatically correct?
That sentence is not grammatical English.
You could say about The Great Gatsby that
It’s one of the greatest novels in American literature.
There is no way to tell without context whether the writer has erred or some words were inadvertently dropped.
Your suggestion of
It's one of the greatest American literature classics.
is awkward even if grammatically acceptable.
It's one of the classics of American literature.
would be better.
You would probably never say "one of the greatest classics" since "classics" are already implicitly "great".
