One of the naturalization exam questions is "What do we show loyalty to when we say the Pledge of Allegiance?" and possible answers are "the United States" and "the flag".
I understand (I think) why there is a "the" for "United States" but don't understand why it is there for "flag". As I see it, it is not some physical instance of flag everyone knows about. So why "the" then?
"The Flag" is simply short for "the flag of the United States of America" -- which, as you can imagine, is easier to say. We use the definite article to indicate the noun is something that is either unique, or already known.
Of course saying "the flag" doesn't imply there is only one valid "flag" in the world. Every country has its own version of "the flag". You have to judge which flag the speaker means from context.
The question on the naturalization exam does raise an interesting point about the ultimate purpose of something like the Pledge of Allegiance. Who are you offering your "allegiance" to? The country as a whole? The President? A symbolic piece of cloth? The laws on which the county is founded? Some combination of all of the above?
But a full discussion of this is probably outside the scope of ELL.
The simplest answer is that flag is a countable noun, which means it has to be a flag, the flag, or flags; you can't say "I pledge allegiance to flag."
As for why it is the definite article, the, it's because it is a specific flag: the one that represents the United States. The does not necessarily mean one physical object; it can refer to a unique concept as well. A flag would mean "any flag".
