"The Royale"
DATA: "Is this significant, sir?" (Holds up a spacesuit on a hangar)
RIKER: "American."
DATA: "Fifty two stars sir. Places it between 2033 and 2079 AD."
What can we draw from this short scene?

Well, at least Riker recognizes the flag. How many of you would recognize a flag from three hundred years ago?
Not unheard of. I'd recognize the old English flag, which was replaced by the Union Jack some many centuried ago.

Data uses 2079 AD, not 2079 CE. Indicating that "CE" is a passing fad.
Thank goodness for that, too. (Bloody PC nonsense....)
BTW--wasn't it Riker who said the years?

From Data's statement there was only one time period when America had fifty-two states.

In 2079 the state count rose above (or dropped below) 52.
Well, seccession is kinda forbidden, as of the Civil War--so it's probably that more states were added.

I believe Puerto Rico is the best candidate for state number 51, any thoughts on state number 52?
Well, after Puerto Rico, there's Guam, American Samoa, the Virgin Islands...I think that's it, maybe more.
D.C. is out. It's kinda implied in the Constitution that the District is supposed to be set apart from the States.

How big will America ultimately be in the future?
A lot of the older novels refer to the U.S. as the United States of
North America--"NorthAm" for short--so I'd imagine it's supposed to dominate the continent in the future.

Picard indicates during "The Defector" that in the 24th century Riker is a American. Is that how Riker identified the flag?
Well, I'd say, considering how important the USA has been in world history, I wouldn't rule out a simple knowledge of basic Earth history.