FIG. 1 is a perspective view of a hair appliance comb attachment from above, showing the new design; FIG. 2 is a front view of the comb attachment thereof; FIG. 3 is a left side view of the comb attachment thereof; FIG. 4 is a top plan view of the comb attachment thereof; FIG. 5 is a rear side view of the comb attachment thereof; and, FIG. 6 is a bottom plan view of the comb attachment thereof.