The Union simply used the 13 stripes flag, although for historical accuracy it would only have 34 to 36 stars during the Civil War, since West Virginia and Nevada were admitted during the war and stars were not removed for the seceding states.
The situation on the Confederate side is more complicated. The flag with the "stars and bars" (circle of stars and 3 bars) was the first official Confederate flag, with complaints that it was too reminiscent of the Union flag.
The Battle Flag of the Army of Northern Virginia has a diagonal cross although it was square. It became common in the post-Civil-War era for people to use the rectangular flag of the Army of Tennessee.
The stars and bars as official flag was replaced by the "Stainless Banner" (Battle Flag in the canton, on a white field) but that looks too much like a flag of surrender so in the end it was replaced by the "Blood-stained banner" with a vertical red stripe on the far end.
https://en.wikipedia.org/wiki/Flag_of_the_United_States#Historical_progression_of_designshttps://en.wikipedia.org/wiki/Flags_of_the_Confederate_States_of_AmericaShort version, I don't really know, whatever you like, because multiple Confederate flags can symbolize the Confederacy and it's become somewhat politically sensitive to display them although historical accuracy reasons usually holds up.
