We are having porcelain floors laid next week in the kitchen, DR, and foyer. There will be 3 layers of flooring removed over the plywood substrate.
Our registers are coming straight up from the floor, and we want to move them to under the cabinets. I just had an HVAC guy tell me he just puts a register in the toe kick and runs duct to under the cabinet. I assumed the duct work would be run right to the register.
Suggestions?

It would work. Basically the cabinet base is a (mostly) sealed box. If hot air went into it, and there was a register to let it out, it would work. I would be concerned about your local building codes. I'm sure you can check with an inspector who can give you the right answer. I would run duct work all the way out.

I have a number of ducts under cabinets.
They were fully ducted out to a register in the kick.
Hank

I'd bet you'd have some losses do to air leaking under the other cabinets ect. but it might be inconsequential.

It wouldn't be that difficult to cut out the cabinet bottom, install the ductwork, and reinstall the bottom.