I’m not an A/C guy, but I have been doing a lot of research on duct work, air volume, etc; and I have made some major improvements on existing duct work systems, on a lot of homes.
You may have to post a little more information as far as the size of you addition, size of the vents, if you’re going to install an air return in the addition, and what percentage will the addition be based on the total size of your house. Also it might help if you state if you will be tapping into the main run at the start, middle, or at the end of the run. Like I said, I’m not an expert by far, but this information might be helpful for the experts that read your post.
Here in Phoenix, they use PVC for underground duck work. You might see what material, (for underground duct work) is code in your area, and go from there.