Despite its name, duct tape is not the best choice for sealing joints in ductwork. In the case of clothes dryer vents, poorly sealed joints pose a serious safety hazard.
The adhesive on duct tape dries out over time, especially in the kind of frequent temperature changes seen in dryer vents; expansion and contraction also loosen duct tape. This can create gaps in the joints of the vent.
As home laundry equipment has moved out of the basement and into living areas, more ductwork is needed to vent the dryer to the outside; this means more joints. Further, vents are often enclosed in walls or ceilings, making joints impossible to inspect.
Gas clothes dryers produce carbon monoxide, a colorless, odorless gas that can be deadly in an enclosed space. The vent carries this gas to the outside and releases it harmlessly into the air, but if there are gaps in the vent, the gas is released into the house.
Gaps in dryer vents can also cause lint to build up, a fire hazard for both gas and electric dryers.
Foil Tape Solution
Use metal foil tape rather than duct tape. It's more expensive but much more durable. The duct itself should also be made of rigid metal to ensure safety.