Easily find products that ship for free with the Ships free tag on Discover.
If you are using Dynamic Shipping, your customers will be charged $0 in shipping for these products and you won't owe anything to the supplier for shipping charges.
If you are on Shopify basic or want to use a Custom Rate shipping relationship, you can request a rate of $0 through proposals. However, know this applies to all products that you sell from a Supplier, not just a specific product. You can learn more about Canal's shipping options here.