Semiotics can be fascinating.
A symbol represents something in the mind of the viewer. Different viewers, different meanings. You can't pick what it represents in someone else's mind.
On the other hand, heraldry, including flags, also have specific, designated, things that they represent. The American flag represents the USA. The Confederate Flag represents the CSA. The Confederate Battle Flag represents....well, officially, the Army of Tennessee. The square version represents the Army of Northern Virginia. It was used by other armies as well. The design was incorporated into the second CSA national flag, so it could be said to represent the entire CSA. There is no CSA anymore, but I think people could be forgiven if they said it represents the area of the country where the CSA used to be.
For me, I'm interested in history, and that interest began by playing wargames. That flag was on some little cardboard counters, or setup areas on the map. That flag will always represent the army to me.
Or, you could just insist that it means whatever you think it means, and you wouldn't be technically wrong, (see the second sentence above) but it would be a bit self centered.