Don't know if you knew this or not but smoking, actually what we call barbecue is believed to have first been done in the Caribbean. The word barbecue comes from the Caribbean native Taino word barabicu, then translated to barbacoa for Spanish tongues then on to today's barbecue in American English.
It wouldn't be much of a stretch of the imagination to find that it may have actually gotten to the Caribbean from Africa along with the slave trade or perhaps even earlier.
People have been cooking meat with fire for thousands of years, that practice, most likely starting in Africa too, along with the development of Homo sapiens or even earlier species. Even Neanderthals are known to have cooked meat with fire.
Where ever it may have started in the world, way back in history when ever it actually got started, in this country at least, it began in the South. Some even say that smoking meat originated in the American South. However, as much as I'd like to believe that, I seriously doubt it. As I said, fire and meat have been used together for far to long in the history of man, even way back in prerecorded history, for it to have taken any where near that long for smoking to have come about.
If nothing else it could have been and probably was entirely accidental and it's not to hard to imagine how. Many types of lodging in the form of tents, tee pees, cabins, lodges etc. though out time all used to have central fires inside for warmth and for cooking. There was little facility made for the smoke from the fire to escape as to allow too much of it out whould have lost too much heat. Often a single simple hole in the roof had to suffice. To me that constitutes the makings of a smoke house right there. Add a little time and a fresh kill and walla a few hours later you have yourself a nice batch of smoked meat. I've gotta think that someone somewhere has been smoking and barbecuing meat, even in Africa for a long long time indeed.