So the general rule is that an article, either definite or indefinite, must be used with any countable singular nouns. We say 'a chair' or 'the chair', for example. But, it seems that when a singular countable noun comes after the phrase, 'kind of', an article is not used. For example: What kind of flower is this? What kind of chair is this? In both example sentences there is no article before the words, flower or chair. Could anyone explain this, please?
I think this is because you have “what” ahead. the question is asking "what kind". In grammar, if a possessive determiner or possessive adjective is put in front of a noun, the articles (a, an, the) shouldn't be used. eg. my book, Tom's chair, etc...
Back to your example "What kind of flower is this?", "what" plays the role as "my or Tom's".
hope this help a bit.
It seems more likely that of flower is a prepositional modifier, and in prepositional modifiers, the noun in the [preposition + noun] combination can be with or without a determiner or quantifier.
The determiner or quantifier will be some sort of adjective modifying the noun to avoid ambiguity. However, where (i) no ambiguity is possible or (ii) if ambiguity does not matter, then the determiner (i.e. adjective) can be omitted:
"He leapt from tree to tree" Here we are not bothered if it is a tree, the tree, my tree, any tree, Tom's tree, etc., the meaning conveyed by "tree" remains the same
The clue is in the OP "the general rule is that an article, either definite or indefinite, must be used with any countable singular nouns" 1. It isn't an article, but a determiner that is required, and 2. it isn't a rule, it is general guidance with the usual slew of exceptions.