Use a proper roof top exhaust hood if you must go through the roof.
Venting kitchen exhaust fan through roof.
If you want to replace the range hood and exhaust fan above your stove and vent it to the outside and the stove is against an interior wall you have several options.
Venting through a roof vent or exhausting them in the attic could cause moisture problems and rot.
The duct for your exhaust fan needs to be run to the outside of the house to remove the chance of a fire hazard.
In either case do not vent into the wall or the attic.
But the rule of thumb is to route it the shortest and straightest path to daylight.
Be sure to extend the pipe up at least 2 to 3 above the roof to prevent snow buildup from causing problems.
Here you see a very good roof top exhaust hood made by ventilation maximum in quebec where they tend to make roof vents taller to avoid being buried in the snow.
Yes you can vent a range hood through the roof using a 6 single wall pipe.
On the outside you will see the wind baffle that prevents snow from blowing in.
If it sits on an inside wall venting through the attic and out is a better option but if it is on an outside wall it is more practical to vent through the wall.
You can buy the proper flashing to install it on a flat roof and a roof cap that has screen around it to prevent insects from entering.
Also be sure to place your kitchen vent at least 5 feet upwards from the eaves of the roof.