'Kava' is nominative but 'čaje' is the genitive form of 'čaj' (masculine inanimate). Because the sentence refers to an amount of tea it is 'partitive' and therefore genitive case. The correct (genitive) form of 'kava' here would be 'kavy', (feminine) but that isn't offered as a choice.
Maybe re-read Blarni's comment: čaje is genitive, so it literally means “of tea I have very little.” “Kava” is nominative and cannot replace “čaje” here; you would have to use “kavy (mám hodně málo).”
Edit: I now realize that you may have got this sentence as a translation exercise. Okramism obviously got it as a multiple-choice exercise with "select the missing word," something like this:
- __ mám hodně málo.
S/he had no translation to go by, only the grammar, and that's what Blarni explains in their comment.
Ignore word order for the moment. “Mám hodně málo” means I have very little, that's the basic sentence which, of course, triggers the question “of what?” The answer is “(of) tea” – “čaje”; you are perfectly right, it's genitive.
So in Czech it could be “mám hodně málo čaje” or, emphasizing the tea, “čaje mám hodně málo.” “Čaje” is dependent on “málo” (little [of tea]), whatever the word order is.