If you can stand losing 3-1/4" out of your 25-3/4" deep cabinets you can run the duct through them.
This rectangular duct is 32.5" in² in area. If you can fabricate a duct 1" or 2" deep by whatever height it takes to make the same cross sectional area, that might work and it would hardly infringe on your cabinet depth. But, people usually don't make ducts shaped like this, and probably for good reason.
Maybe you could run several small round ducts to make up the duct area.
This hood has uses up to 300 CFM, which would be an air velocity of 300/[32.5/144] = 1400 FPM in that duct. I'd think air moving that fast would be noisy.
You might want to use Engineering ToolBox
or other sites to check how well different duct shapes will work.
Maybe at the distant end you'd need a booster fan.
Work all this out before you lift a hammer.