Since burning coal leads to a variety of air pollutants, presumably a coal mine fire would also lead to air pollutants. My question is whether there have been any published studies on the emission rate of SO$_2$ from a mine fire, such as the Centralia fire in Pennsylvania?
All coal deposits are different. Coal chemist is highly varied, and the amounts of sulfur and heavy metals with the coal seams varies with each deposit & within seams. This is due to the conditions prevalent when the coal seams were formed.
Consequently, the amount of sulfur dioxide emitted when coal is burned, whether in a power station or a mine fire depends on the amount of sulfur in the deposit the coal came from.
Without having an assay of the amount of sulfur in the coal or measuring how much sulfur dioxide is generated in a fire it is impossible to know how much sulfur dioxide will be produced.