Hello amok569,
Most if not all dropshippers offer flat rate shipping some even (if you're lucky to find them) offer free shipping.
You can base your shipping cost on your dropshipper's offered rates. Some resellers knowing that their dropshipper offers a flat rate shipping for their products will add the shipping cost to the item's price in their listings and advertise/list their items as "free shipping" to entice customers!
Make sure you check your dropshipper's shipping policy/rates before you start selling items, so you are clear what action to take.
You can learn more about drop shipping in the guides below -
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Hope this helps!