This is what they call the person bearing the flag at the Olympic games, the group who are with the bearer are called the delegates. Of course the context here is school, but the term is still "flag bearer"

"Modern color guard has evolved over the years into a form of entertainment similar to dance theater. Color guard can be found in most American colleges, universities, high schools, and independent drum corps. Color guard uses props, along with movement, to express dynamic passages in the music accompanying the marching band show."
https://en.wikipedia.org/wiki/Color_guard_(flag_spinning)

"In the military of the United States, the color guard (where the word color is referring to the national flag) carries the National Color and other flags appropriate to its position in the chain of command."
https://en.wikipedia.org/wiki/Color_guard#United_States


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Note added at 1 hr (2015-10-16 15:27:29 GMT)
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My suggestion is just an option because the context given is not clear enough.

If it is just the person:

https://en.wikipedia.org/wiki/Standard-bearer