You may not want to restrict your convection air with the corrugated round duct coming off the stove. It looks like it is only about 8" or so. The 1000 cfm blower, I would think, should blow much more air than what the round duct can handle. Might as well take advantage of the maximum output of your stove and blower and put in a rectangular plenum that fits over the koker's opening, then run large enough duct(s) from the plenum to the existing duct work in order to take full advantage of the blower's capability.
On the attached picture, I have two 8 x 16 ducts coming off my plenum, and that is with a 1500 cfm blower. I would imagine at the very least you would want a duct size equivalent to an 8 x 16 so there is little restriction in the air flow from the stove to your existing ducts.