As I am sure you have discovered, Krystian, relevant references to "broken meal" are hard to come by.

Given the reference to the "German War", and the fact that Wiley recorded this song in 1930, the most relevant definition of "meal" is probably Webster's from 1913:

"1. Grain (esp. maize, rye, or oats) that is coarsely ground and unbolted; also, a kind of flour made from beans, pease, etc.; sometimes, any flour, esp. if coarse.
2. Any substance that is coarsely pulverized like meal, but not granulated."
http://machaut.uchicago.edu/?resource=Webster's&word=meal&us...

This doesn't really add anything major, but it confirms how the word was then used. Unbolted, but the way, means unsifted: "bolt: To sift or separate the coarser from the finer particles of, as bran from flour, by means of a bolter; to separate, assort, refine, or purify by other means".
http://machaut.uchicago.edu/?action=search&word=bolt&resourc...

"Broken", in relation to grain, means very coarsely crushed; you can find many references to broken rice, broken wheat and broken maize/corn. So "broken meal" is almost a tautology; it must mean very coarse meal.

So there is an obvious contrast between refined flour and course broken meal, with implications which Tony has referred to and do not need further comment; plainly the flour/broken meal contrast is parallel to rich/poor and refined/unrefined.

However, there may possibly be other connotations there too. First, just let me mention in passing that "broken meat" (not "meal") is a Biblical expression, referring to the leftovers in the Parable of the Loaves and Fishes in Matthew 15:37 ("And they did all eat, and were filled: and they took up of the broken meat that was left seven baskets full") and Mark 8:8 ("So they did eat, and were filled: and they took up of the broken meat that was left seven baskets"). This is from the traditional Anglican King James version of the Bible. I mention it simply because of the possibility that, since the Bible text is so extremely familiar in the American South, there might conceivably be an echo of it here. I don't think it's likely, but it would add a Biblican connotation: "broken meat" was the plentiful remains of a miraculous meal, the fruit of divine bounty. Just to bear in mind.

More relevant, I think, is the possibility that this might be associated with grits, an emblematic Southern US dish made from coarse maize/corn meal. The name "grits" comes from Old English grytt, meaning coarse meal.
http://en.wikipedia.org/wiki/Grits

This is an attractive possibility, because it would add a strong affective dimension of "coming home": he imagines himself, when dead, bringing them the most basic, humble but much-loved home dish. This bill from South Carolina declaring grits the state's official prepared food is quoted in the Wikipedia page:

Whereas, throughout its history, the South has relished its grits, making them a symbol of its diet, its customs, its humor, and its hospitality, and whereas, every community in the State of South Carolina used to be the site of a grits mill and every local economy in the State used to be dependent on its product; and whereas, grits has been a part of the life of every South Carolinian of whatever race, background, gender, and income; and whereas, grits could very well play a vital role in the future of not only this State, but also the world, if as Charleston's The Post and Courier proclaimed in 1952, "An inexpensive, simple, and thoroughly digestible food, [grits] should be made popular throughout the world. Given enough of it, the inhabitants of planet Earth would have nothing to fight about. A man full of [grits] is a man of peace."