Question

What is the function of the noun clause in the sentence "Many wonder why superhero flaming carrot wears flippers"

Answer 1

Direct Object. 

Hope this helps you.

Answer 2

i'm not super smart or anything but  noun clause is a dependent clause that acts as a noun. Noun clauses begin with words such as how, that, what, whatever, when, where, whether, which, whichever, who, whoever, whom, whomever, and why.
 So maybe the noun clause is why superhero flaming carrott?