The shipping functionality is being handled by WooCommerce. So you are free to use any WooCommerce compatible payment gateways with Dokan. WooCommerce already has some built in shipping gateways, these can only be configured by the admin and will work for each vendor. The vendors will not be able to configure any shipping charges if you use any shipping gateway other than Dokan Shipping.
To know more about how WooCommerce shipping gateway works and how to configure them, please read their official documentation.
Dokan plugin has the most advanced feature to enable the sellers to add shipping costs from the frontend. Using this feature is optional. If you do not like this feature and want to use the old school WooCommerce shipping classes, then no action is required.
The state based shipping option of Dokan plugin can be found on wp-admin -> WooCommerce → Settings → Shipping → Dokan Shipping.
Click on the enable checkbox and hit save. If you want to apply taxes on then you can select taxable else you can select none.
The job of the admin is finished here. Now the next job is to the sellers.
To use the state based shipping feature of Dokan plugin, vendor has to navigate to Dashboard → Settings → Shipping
More detailed information about configuring the shipping option, please read How to configure and use Dokan shipping