The calculation itself is pretty straight forward to make using the Stefan-Boltzmann law but we have to make some assumptions. I assume that the emissivity of the original aluminum bottom of my boil kettle is 0.07 which is the reported literature value for aluminum. I further assume that with the black engine paint in place the emissivity is 0.9 which also seems reasonable based on literature values (
http://www.infrared-thermography.com/material-1.htm). Finally we have to assume the temperature of the propane flame beneath the kettle. I'm less sure of the true average value here so I'll use the peak flame temperature to give a best case scenario. Realistically we know that the average temperature below the kettle's surface is less than this so the difference in blackened vs. silvered is less. Also, my boil kettle has an outside diameter of 13.5" which is what I'll use for my calculations.
Given all the above, the original surface experiences a radiative heat gain of 9,611 watts. When blackened the same surface experiences a radiative heat gain of 123,576 watts. My burner is rated as capable of putting out 185,000 BTU/hr which is only 54,000 watts. Clearly my assumption about the average temperature below the boil kettle is way off but you get the idea. You get drastically better heat transfer to the kettle which should give you significantly shorter rise times.