Don't vent a gas dryer into your house: critical points.
The most dangerous byproduct of natural gas (methane) combustion is carbon monoxide (CO) rather than carbon dioxide (CO2). CO2, a byproduct of mammalian respiration (breathing) is exhaled and heavier than air, in beer and soda. Carbon monoxide, on the other hand, displaces oxygen in hemoglobin and is toxic. Many people have died from this. This is a critical point. With natural gas appliances one should always have a carbon monoxide (CO) detector.
Also, cotton dust does not cause cancer. Non-biodegradable particulates such as silica (silicosis) and asbestos (asbestosis) are linked to malignancy formation such as mesothelioma. Cotton dust can be an irritant, yes, but your body can deal with cotton dust. .
I deeply respect the knowlege offered by this website, but sometimes misinformation can be misleading and downright dangerous. Bottom line, don't vent a gas drier into your house.