Latakia is fire-cured using different firing woods than traditional fire-curing, but the technique is pretty much the same. For "Kentucky" fire-cured, for example, oak and other hardwood slabs and sawdust are used. So my home-made chamber for making Latakia would be the same (unless you intend to use and entire shed).
Making Latakia at Home PART 1 (of 3) Background I have fire-cured various tobaccos in a trash can smoker (placed on top of a Brinkman smoker), using an assortment of woods: hickory, oak, maple, apple, etc. Each tobacco variety combined with each of the woods that I tried produced some...
fairtradetobacco.com
The requirement is simply a smoker (like you might use for smoking fish or ham) where the tobacco leaves can be exposed to the smoke without burning.
Simple fire-curing takes about 3 weeks of firing, though you can adjust the duration to the extent of smokiness you prefer. I would begin with fully color-cured leaf.
I used to have a full thread on that in the howtogrowtobacco.com forum (now dead, though an archival copy is still viewable), but I can't locate that thread in the archive.
Bob