To follow up on William Kurtz's reference to civil war data: I've found uadata.org to be a more reliable source than civilwardata.com. 16% of the black troops in the uadata "extended" sample are listed as drafted, whilst the majority (54%) in that sample are listed as substitutes. If we combine the "extended" and "original" samples then only 7% of all black troops were drafted and 24% were substitutes, the majority being volunteers.
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Professor Oakes writes: "I have another suspicion that I can't document just now. I wonder if the original request for information about Fry's policy was driven by Congress's dissatisfaction with the fact that slaves were not being drafted in Kentucky. If so, Fry's response may have led Congress to be more explicit. "
Based on two letters found in OR ser 3, vol 3, I think Prof. Oakes is exactly right.
I tried to make this point earlier. As far as I can determine there was no Militia Act of 1863. On March 3, 1863, Lincoln signed the Enrollment Act of 1863, which entirely bypassed the militia system. This law established a federally managed system of enrollment of draft eligible men, held the drawings, and chose the draftees. The confusions and failures of the Militia Draft Act of 1862 had left northern governors with little appetite for attempting to enforce a militia draft.
For what it's worth, I just came across a letter that may be relevant to this discussion. One black Philadelphian wrote in April 1863 that he "was enrolled for the draft which will take place in about a month." He further noted that "Many colored people are alarmed and others declare if they have to go they will enlist in the Mass. Reg. as there is no provision made by this State for the families of colored soldiers." "Letters of Negroes, Largely Personal and Private [Part 1]," The Journal of Negro History, Vol. 11, No. 1 (January 1926), p. 84.