You would normally use a leg kit which the cooler would be attached to then the bottom of leg kit would be nailed or screwed to roof under shingles or other roofing material.
How to install evaporative cooler roof jack.
Cooler installation kit note.
Set cooler in position on roof jack.
Use roof tar or waterproofing membrane to seal all openings.
Installed swamp cooler on roof.
Install a flexible duct from the roof duct to the ceiling register.
Install a duct transition piece if needed for a round flexible duct.
Select a leg kit that fits your cooler model and follow the cooler and leg kit installation instructions.
Install supporting leg kit.
Apron collar and flex duct not shown sheet metal slide in damper for winter use only large cover plate small cover plate barometric damper roof jack assembly rja 12 horizontal run level vertical rise roof.
Any screws used to mount brackets to the roof should be coated with tar to prevent water entry.
Install the cooler duct a power wire and a thermostat wire leaving excess wire to allow a thermostat installation inside the home.