Usually you want to run the 3x10 rectangular duct work. This fits neatly in the walls between 2x4 studs and both the standard intake and exhaust for the range hood tend to assume this size. I don't believe you can use any flexible duct work on the kitchen hood because of the grease buildup. Any hvac guy should be able to do this for you, but in general they hate working with the rigid ducts these days. If you already have an HVAC guy then call them first. If you get a lot of push back then find someone more willing to do the work.
Before you start you should see if the hood will be placed in the center between two studs (best case). I think you need to tear up the wall and frame it out like a window if there is a stud running right in the middle. You don't have to run the ducting through the wall. It can run through the cabinets. Also, I think there are some code requirements (like adding straps or something) if they run through the wall and cut the sill plate at the top in the attic. These kind of complications are why a simple few feet of ducting gets shockingly expensive and lots of HVAC guys avoid doing it.
Yeah, I'd have to use rigid ducting for the reason you mentioned. Flexible ducting + grease is bad times.
Due to idiosyncracies of my kitchen, it's a whole lot easier to use a wall mounted hood and run ducting directly up through the ceiling than dick around with rectangular ducting between studs. If there was a finished room above the kitchen, ducting between studs would definitely be the way to go. Since it's just a cavern of an attic, it's waaay easier to just duct through an attic and out through a wall.
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