Where does your duct need to run?

I have a similar ceiling above my range. I have an undercabinet hood and cabinets to the ceiling, ductwork inside. It's sort of like what you have with an extra, triangular patch of cabinets on top.

I would think the same way you would vent with a flat ceiling.

Straight up. This is the roof. The bathroom is on the other side if the wall so it has to go out the ceiling. Can you post a picture of your kitchen please.

Without bringing up at the moment the requirements for the hood, blower, and other parts, you can run the duct within cabinets as noted, or use a stainless steel duct cover cut to fit the ceiling. It may be neater to cut a square hole through to the attic and drop a rectangular duct cover down to the hood. If there is no attic, what is the distance from the sheetrock to the roof underlayment?

If you don't want cabinets above it, a chimney hood would look nice. They have "pretty" chimneys to cover the duct.

This is the "I'll never give up an inch of cabinet space" approach. The bottom row of cabinets lines up with the 8' ceiling at the end of the slope. The top row is not used for everyday storage so no knobs. You have to open the lower cabinet to pull them open which works fine. You can tell by the dust line on the hood how high I can reach. I guess it's time to pull over a stool...

The hood vents up.