It's an HVAC contractor who can help you, since it will be a matter of setting up ductwork. You need to have the kitchen exhaust duct be 8" or 10" diameter, not smaller, not bigger. Make sure to ask prospective contractors about what size duct they can install given the home's structure as mentioned in the above comment.

You will also need a contractor for the opening that exits the house - i.e. if through the roof, a roofing contractor to lift shingles, flash around the vent through the roof, and roof cement for re-attaching the shingles. Or, if the vent goes out the side of the house, you will need similar work but instead of roof shingles, it would be your siding whether that is shingles, brick, vinyl siding, or whatever it is - the contractor that would install that type of siding would be the other contractor you'd need. An HVAC contractor that regularly installs kitchen exhaust venting may have preferred roofing or siding contractors they work with, so that would be a question to ask them.

How high does the centerline of a horizontal duct need to be? The kitchen ceiling is 7’6”; I am not sure what is in the 6” above it since the other first floor ceilings are about 8’.