You can vent into the chimney, especially if your attic has vents out to the outside. There should be a cleanout at the base of the chimney that you can jam your duct into, or better still, find or make a 6" hole higher in the room- there might be something from where an old furnace was once attached.
Can you seal over the dirt floor? Pour concrete? Dirt harbors mold spores and will be a place where pests can breed.