for it don’t strengthen the army, but takes one away for every colored man enlisted.
Frazier disagrees with the idea of men of color being used as 'substitutes' in the army. By using soldiers of color to replace white soldiers, it diminishes their efforts and want to enlist in the armed forces. It creates a race-based hierarchy in the army.
State in what manner you think you can take care of yourselves
I found the phrasing of this question to be interesting and indicative of the time period. By asking 'how they can take care of themselves', I think it looks down on the freed people and implies that they cannot take care of themselves
And to assist the Government, the young men should enlist in the service of the Government, and serve in such manner as they may be wanted.
Despite giving a way that emancipated men could assist the government, I think the phrasing of 'serve in such a manner as they may be wanted' shows that Frazier knows that racial inequality would continue. Even though they would be serving their country like any other soldier, he knows they will not be treated the same.