In my opinion, the symbolic meaning here has to do with the image we have of the eagle. As the national symbol of the country, the eagle is associated with courage and bravery. I think that this is the symbolic meaning it has in this poem.
In addition, I think the colors have a symbolic meaning. I see the red being related to blood and battle, but I see the gold being related to glory.
By having this as the symbol of the regiment, Crane is talking about how the men are conditioned to drill and die and show their courage, all for the sake of glory (which he does not believe they actually get).
In Stephen Crane's "War is Kind," the mighty symbol of war and courage, the eagle "with crest of red and gold" is made a mockery of by the dying soldier behind it who tumbles into the yellow trenches, "Raged at his breast, gulped and died." Thus, there is a perversion of the glorious colors of the flag as the gold degenerates into the yellow [symbolic color for evil] trenches and the raging breast of the soldier is red from blood as the soldier dies.
Clearly, the symbolic meaning of the flag--courage and glory--becomes sullied in Crane's bitterly ironic poem with contrasting images that suggests not honor, but the tragic outcome of war.