That's an interesting question, as I don't recall Tolkien ever describing the tobacco flavors themselves. I have smoked an "Old Toby" from a couple of different blenders, and never the same thing twice. I would bet that Gimli would be smoking a meaty Latakia, the Hobbits puffing on infused tobaccos with maple or honey flavors, and Aragorn smoking something fermented like
Perique. Myself, I think Frog Morton on the Bayou in an old Clay Churchwarden would be keeping in the spirit of things.