The previous photo was actually the old chimney - these pictures show the replacement. I'd agree with the flashing explanation if the stained area was confined to area down to roofline. It extends further out however suggesting a source from higher up. These are the numbers from boiler tune up a month ago:
Weil Mclain WTGO-7
Gross Stack Temp 460
Net Stack Temp 400
CO2 % 12
Breech Draft .04
Overfire Draft .01
From the height of that stack those stains are not coming from the gases at the the top.
in the pic's it looks as if the collar may have some discoloration another thing I have done is to cote the pieces with "spray on plasti dip" and I dont think it would be good on shingles but a watered down sulfuric acid will remove the stains so try it on a scrap piece?