Depending on the multi-vendor mode enabled for the store by the administrator, vendor users may or may not be able to choose which shipping methods should be available for their products:
In the "Warehouse" mode, the configuration of shipping methods is the job of the store administrator, whereas vendors do not have any shipping management capabilities. They do not need such capabilities since the shipping fee for orders from more than one vendor is calculated for delivering all products in a single shipment from a single warehouse location.
In the "Vendors as separate shops" mode, each vendor configures their own shipping method(s). The management of shipping methods by a vendor user takes place in the Shipping Methods section (Store Setup > Shipping) of the Vendor area.