How did the "smokers" have all of those cigarettes in Waterworld?

Not all smokers smoke cigarettes all the time. I never assumed this was their defining trait, I always thought of the use of engines burning oil as namegiver compared to the drifters who sail or the archipelago people who mostly use paddles. Still a lot of smokers smoke cigarettes or cigarillos of different kind. They don't seem to be very valuable; on the other hand they are a special gift that Dennis Hopper's character gives away on his tour through the ship. He throws them into the people like candy on a parade.

We don't know much about the economy of Waterworld. We also don't know much about the time frame. There are contradicting indicators for how long after the flood the action takes place. The flood probably didn't come suddenly so people could retracted to higher areas before leaving land completely. They probably would have taken a lot of stuff with them, and cigarettes are a valuable currency in times of trouble by experience (e.g. prisons, after devastating wars like WW II in Germany). So people may have saved them. Also everything aboard a ship isn't directly affected by a flood. (And can't you dry wet tobacco? The quality may be stained but that doesn't seem the main problem.) So depending on how long after the flood the action takes place those may be stock. The smokers are reavers as we see in the movie so it mustn't be just their own stock from the beginning. How plausible this is depends highly on the timeframe. There are indicators that the action takes place shortly after the flood (still floating ships, paper) or long after (mutation, reference to former generations).

We know that some material is produced and recycled. When the interior of the Exxon Valdez is shown we see repair crews and even metal casting. The drifter from the beginning in the movie mentioned that the slavers now produce epoxy in good quality. So we know there is some production activity. We don't know whether cigarettes are produced and from what they are produced. It is possible that they are recycled filters with seaweed filling but we neither see collection of cigarette butts nor do we learn about this.

The movie doesn't give a definite answer. Some ideas seem plausible within the few bits of universe that we see in the movie but a definite answer is not possible.

The "smokers" seems to be largely surviving by raiding settlements and passing vessels. Particularly prized items of booty are petrol (obviously) as well as cigarettes and booze. These are luxury items that seem to have survived from before the flood and were, presumably, highly prized by the original owners as tradeable goods, something confirmed by the film's official novelisation, itself based on the original screenplay.

On the outskirts of the battle, on the deck of the oil-drum-strewn refueler barge, leaning on his mace of office—a Spaulding five iron—the Deacon inhaled his unfiltered smokestick. Back on the 'Deez, the mother ship, he had in his storehouse of spoils many cartons of the prehistoric sticks—Camels, Marlboros, Chesterfields, all fresh enough to smoke after hundreds of years, thanks to their crisp, crackly plastic wrappers. The ancients had been very wise.

I'm struggling to work out why you'd think that anything from before the flood must have been submerged when it would seem far more likely that the "Smoker"'s cigarettes and vehicles were found on board watertight vessels they raided.

With increase in the sales price of cigarettes millions of smokers have gone back to rolling their own. Zig Zag Cigarette Tubes are the most popular brand of filtered tubes for this purpose and are manufactured by a French conglomerate. Perhaps the Smokers came across a single cargo container ship which would have contained Billions of Zig Zag Cigarette Tubes and cans of loose tobacco. What better "make work" for idle pirates and stowaways than sweatshop cigarette rolling?

I think its obvious that the smokes,oil,booze is coming from the smokers tanker. you can see the freight boxes on the deck so i can only assume its all leftover freight that never got to its destination. no seaweed smokes and other speculations. its too obvious.