This help page explains our discount settings:
You can use the same Discount Code for multiple discounts, such as a discount on the item and a discount on Shipping, as long as you remember to give each discount a unique Discount Name (as that's how our system distinguishes one discount from another). The buyer would only need to enter the code once to apply all discounts which match that code.
However, we have no way to create a discount that eliminates shipping charges on one particular product while leaving shipping charges unaffected for other products. If this is what you need, you might consider whether you could include the cost of shipping in the item price to offer "free shipping" to everyone for that item.