Hi, Tracy and welcome to permies!
I don't see a stove pipe in your picture, if you don't have one tall
enough that would keep it from drawing well. We cooked and canned on a wood cook stove outdoors every summer for several years.............it was hot but better than cooking in the cabin over wood in the summer.
I think if you get a good draw with enough pipe and some nice split dry good burning wood, it shouldn't smoke out any cracks.
We ran our pipe up pretty high because there were quite a few
trees right around where we had it set up. On some stoves we sealed what cracks we could with a paste of ashes and salt, I think............that has been a longgggggggggggg time ago so don't try it without some research