You can find products that ship for free using the Ships free tag on Discover.
If you are using Dynamic Shipping, your customers are charged $0 in shipping for these products and you don't owe anything to the Brand 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, this applies to all products that you sell from a Brand, not a specific product. Learn more about Catalog's shipping options.