First, users must have Advanced Shopify or Shopify Plus plans or yearly billing. See link:

Third-party carrier-calculated shipping rates 

Also check out these links to set up backup rates. Learn more about backup rates in the Shopify Help Center, or customize backup rates in your Shopify Admin. 

1. Check the "Enable live shipping rates" from the Order Synchronization Tab, and also follow the guide on how to setup the shipping zones.

2. In Shopify Settings, under "Shipping and delivery"click "manage" under the general rates, then add the rate from the created shipping zone. 

3. Select "Use carrier or app to calculate rates", then select the "Turn 14 Distribution API (Rates provided by app)", then click the done button. 

4. See if the "Turn 14 Distribution API (rates provided by app)" is added. Click the save button.

5. (Optional) In Turn 14 Distribution App,  you can add a margin to live shipping cost from the Pricing Tab. Click the Save button.


Here is a sample output of live shipping rates.