The flag's a bit off; the USA only had 48 states in Sara's day.
Yes, but KanColle is supposed to take place in the modern day with girls that "have the spirits of warships", so modern flags can certainly be appropriate. (The Japanese ships are drawn with the modern flags, as well, since there's a similar, if lower-key controversy involving Chinese and Koreans with the Imperial Japanese Flag in modern Japan as the swastika has...)
(The Japanese ships are drawn with the modern flags, as well, since there's a similar, if lower-key controversy involving Chinese and Koreans with the Imperial Japanese Flag in modern Japan as the swastika has...)
The "rising sun" flags (there were two slightly different variations, one with the sun centered and one with it off a little to the left) were the Imperial Japanese Army's battle flag and the Imperial Japanese Navy's ensign, respectively, and so became conflated and collectively identified as "the Imperial Japanese flag" by Allied forces in the Pacific, since they were seen flying from IJA positions and IJN warships.
In fact, though, they were no such thing--the version without the sun rays has been the Japanese national flag by law since 1889. Its use as the national flag became quasi-official after 1945--one of the many details of the national identity left in a sort of legislative limbo by the end of the war and the American occupation--until the Diet got around to reaffirming it (and the national anthem) in law in 1999.
Which is not to say that it isn't still controversial* in the region--all three flags are; merely to note that the plain disc-on-white version is not anachronistic in a 1940s context (unlike the modern German tricolor, the Italian flag without the arms of Savoy, or the 50-star US flag).
As for when the game is set and whether it's appropriate for the characters to display the colors of (in many cases) countries that succeeded the ones their archetypes were actually from, that's fair enough. For myself, I think it's a bit weird to see the likes of Prinz Eugen associated with what my Cold War-vintage eyes still see as the West German flag, but I don't particularly want to see her sporting the Hakenkreuz either. I prefer to cross the streams and think of her and the other German ships as coming from Karlsland in the Strike Witches universe anyway. :)
* Heck, the Maritime Self-Defense Force's ships still fly the rising-sun ensign, which I'm sure thrills the neighbors.
