I am not certain that your hypothetical is one that would exist in the real world. Flours start out at the miller's facility at a particular level of moisture, which can then go up or down depending on how it is stored by the distributor and ultimate end users. Assuming for purposes of your hypothetical that both flours started out at the same levels of moisture, you might complain that the total weight of the flour in Bag B is less than that of Bag A, but apart from the fact that some labeling law may be violated, the only real difference is that the flour in Bag B will be drier than that of Bag A. The difference in a practical sense can be overcome by simply using a bit more water when using the flour in Bag B. Your question implies that you know the moisture content of the two flours. In my experience, that kind of information does not appear on packaging materials, although it is usually available from the miller or distributor.
You might find it of interest to see how grains are actually milled to make flour and how beginning moisture levels are established. I did some online research and found the following description of that process:
Flour is composed of flour solids and moisture. The average water content of wheat kernels used to make flour is 12.5% by weight, with a range from 10% to 14.5%. Efficient milling practice requires adding water to raise the moisture content to 15% to 16%; if the wheat is too wet or too dry, milling will be hindered. During milling, the moisture content is reduced to 13% to 14%. The moisture content of flour does not remain constant after milling is completed. If the relative humidity of the atmosphere in which it is stored is greater than 60%, flour will gain moisture, and if the humidity is less than 60%, it will lose moisture. The federal net-weight labeling standard permits variations from stated weight caused by this gain or loss of moisture.
Tom Lehmann says that within a couple weeks storage in an air-conditioned facility, the flour will dry down to about 11 to 11.5% moisture content and that under normal conditions the flour won't dry down below 10.5% moisture. I have seen instances where people have increased the water content in a dough formula by at much as 25% to compensate for an alleged deficiency of moisture in the flour. From what Tom Lehmann says, in reality the difference due to a loss of moisture is but a few percentage points.
I might add that some imported flours have a beginning moisture of as much as 15.5% (the San Felice Italian flour is one such example). Grain/flour experts will tell you that when you get above about 14% that is too high a level and increases the risk of mold development and insect infestation. I suspect that that is not a real problem for bakers because they go through flour at a fast rate, and the efficient ones will usually date their bags of flour to be sure that they are used on a first-in first-out basis. A home user might be concerned if he or she has a 55-lb. bag of flour and lives in a warm and humid climate. Under these conditions it might be a good idea to consider the above factors in determining how best to use and store the flour.