The most likely reason why Frederick Douglass said that black soldiers will “wipe out the dark reproaches” directed at blacks “by our enemies” was that the Civil Rights agitators such as Harriet Tubman, Martin Luther King Jr and many others would be successful in ending slavery and systematic racism.
It is important to note that your question did not include a prior passage or article but it is highly unlikely that he literally meant black soldiers as real soldiers, but that he meant the soldiers of Civil Rights agitations would successfully wipe away the reproach which the white man had put on them with racism and systematic segregation.
The "enemies" here refers to white men
"Black soldiers" meant Civil RIghts agitators
"Dark reproaches" here meant racial segregation.
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