Explanation
In a sentence, the verb is used according to person and number.
In the case of the following words, the verbs used will be singular:
Each, every/everyone, someone/somebody, none/ nobody, one, any, Many a, more than one, etc.
For example:
Everyone are addicted to smartphones nowadays.
Everyone is addicted to smartphones nowadays.
The phrase 'Many a' is always followed by a singular noun i.e. flower (in this case).
As per the rule and phrases given above, 'a' will be used in the blank part of the given question.
Correct Sentence: "Many a flower is born to blush unseen."