Yes, both exterior chimneys. Paper and kindling works for the VC, super cedar fire starter works for the BK.My cookstove is like this. I've tried a few top down starts with mixed results, could have been the wood quality on the smokey starts. What works best is leaving a propane torch in the firebox for a bit followed by a kindling fire and then finally I can put real firewood in. Perhaps next year when I have even better seasoned wood and more experience the cooker will go smoother.
Do you have an exterior chimney? Once my cooker goes cold I think the exterior chimney becomes an intake for my interior chimney even when it's not burning.