The poem looks at the hidden labor behind symbols we take for granted. Flags usually stand for pride and belonging, but here they come from children who work to produce them. The speaker doesn't shout about this. Instead, the tone stays flat and observant, which makes the scene feel colder.
The images are striking. Dull eyes are compared to organ keys that have been pressed down and can't be made to "whistle," as if the children have been worn out of their liveliness. They are "quiet" and "will do as bid," words that sound like what an employer might say about useful workers. The speaker seems to be quoting that attitude in order to expose it.
The last two lines turn strange and open. A river becomes "a letter from an unknown hand," which suggests a message from someone we can't see or name, much like these children. The mood is uneasy, restrained, and quietly accusing.