Your answer is A: "As a courtesy, most ships usually fly the national flag of whichever country they are visiting". In order to identify the complements a verb selects, you should take into account verb patters.
First of all, you identify the main verb. In this case, it is the verb "to fly" in its transitive form (somebody flies something). The NP "most ships" functions as the subject of the sentence and "the national flag of whichever country they are visiting" is the D.O (direct object). The IP "whichever country they are visiting" is a subordinate clause which functions as the object of the PP (prepositional phrase) "of".
