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Have you read the pledge? The flag stands for "the republic". It is a pledge to the United States itself...

I think you're confused. The first objective clause is pretty direct.

"...the flag, and to the republic for which it stands

Right. The flag and the Republic.

Individually and collectively perhaps, but not only the Republic.

I guess it depends on the definition of "Stands". If it literally means the flag standing up, I guess you're right.