Shopify separates the two locations into sub-carts and returns a rate for both, and adds them together and that is what is displayed. No app can solve this issue when the store is operating under 2 or more profiles.
There is a work around inside our app Intuitive Shipping. The client would need to have all products under 1 profile, and create Scnearios (these are the rules or restrictions) for when products are in location A and Location B. With our advanced blending, we can blend these two rates together and display just the flat $6 (and much more if you need). Please have a look at our website, and if you feel this would help benefit your client and their customers, please book a free Demo.
Please note, any rate providing app does require a feature called Third Party Calculated Rates to be enabled. This a requirement from Shopify. Depending on your Shopify Plan Level this could be available to you for free.
We seemed to have found a solution for this problem of double shipping rate due to multi-location. Using our ShipMagic app’s Shipping Customization feature, you can actually setup rules such that double charging of the shipping cost is avoided.
This solution works even without CCS (on all Shopify plans). But it only works if you use flat rate shipping.
You can install the app from here and reach out to live chat support for more information on how to setup the app.