As a footnote to Nick ************'s very thorough discourse, I would note that various shades of gray woolens can of course be achieved without dyeing at all. But where such coloring was called for, dyeing in the piece was indeed less expensive for contractors than dyeing in the wool, as there was some fiber loss in the spinning process (which was performed by externally powered 'mules'--not treadle spinning wheels) as well as the weaving and finishing phases of production (fulling, shearing, plating). Hence, in cases where a large volume of fabric is being considered (as in these contract scenarios), the savings of piece-dying could be substantial. And while it is not the case in this particular instance, if the dyestuff happens to be indigo (blouse flannel, sky blue kersey, etc.) the contractor's savings by piece-dyeing could be enormous.
Please note that the statement in the article cited that "The 1865 'Quartermaster's Manual' (unpublished), codified flannel specifications" is not accurate. As this text was never published, it didn't "codify" anything--indeed, no one ever even saw it! As I have stated previously on this forum, this important manuscript does establish an intent on the part of the QM Dept. to codify these specifications, and it is useful for research so long as we understand that it is referring to an ideal that is based upon "lessons learned" in the Real World. It represents what the government would like for the stuff to look like from 1865-on, not what it actually did look like during the war years.
"Great spirits have always experienced violent opposition from mediocre minds." Albert Einstein