Are you in a ranch or 2 story home? Does your range sit on an exterior wall?
Most construction is platform framed. Which means that at every floor, there will be a double 2x4 that supports the floor, and then the attic above it. If you go through that wall cavity, you will need to cut through these. And ask me how I know, but they don’t always line up with the joists above! So you may have to tear out drywall just to find out you can’t do it.
Also, if it’s an exterior wall, you will have to remove the insulation to hardpipe up the walls. Typically, you don’t mess with your insulation envelope of the home. I don’t know about this exhaust pipe, but your hvac supply runs need to have a minimum Rvalue of insulation between the duct and outside wall.
So, if it’s 1st floor kitchen, with 2nd floor and then attic, you will need to tear out the drywall on the wall through the entire run, tear out some of the ceiling drywall at each floor, cut out the double top plates at each floor, and hope to hell the joists and rafter ties sit right on the 1st floor studs, AND hope the 2nd floor wall studs sit right on that too. Then, you still have the insulation to take out and replace according to local code. Then duct through your attic to get out of the roof not at your eaves.
Now, if your house is balloon framed, you may have an easier time to run this ductwork. BUT then you have a bigger issue overall because there wouldn’t be any fireblocking.
All of this to say, holy hell what a pain in the ass! Go out the side wall! Unless you designed and built the house to accommodate a vertical run up, stay far away unless you want a major rehab project.
Sent from my iPhone using Tapatalk