http://guillermo-rein.blogspot.com/2016/06/erc-haze-reducing...
If I'm understanding the sources correctly, the coal seam on fire in Centralia is about 3700 acres in total size, and coal seams seem to be only a few feet thick generally. Plugging in 8 feet for a thickness (which I think includes a large amount of non-coal rock, but I don't know the recoverable fraction so I'll estimate 100% of it to be coal), I get that the total CO2 production of burning all of it would be about 7 million metric tonnes of CO2. That would be for the entire lifetime of the fire.
So one coal seam fire would produce about 0.2% of the US's yearly CO2 emissions. Keeping in mind that these fires last for decades, that would suggest that coal seem fires account for less than 1% and probably less than 0.1% of CO2 emissions.
I'm saying put it out. Less CO2 released.