The high efficiency furnaces are making chimneys obsolete. In order to vent the hot water heater after installing a high efficiency furnace,, the chimney has to be "lined". Basically a flex duct inside the chimney. The water heater cannot be in the chimney alone. Apparently, the water vapor can freeze.
So, you may be able to vent a generator through a liner.
So, you may be able to vent a generator through a liner.