Here is what is working for me:
It would appear that Shopify assumes you will carry out multi-location fulfilment in this way and only charges the single rate.
The only problem with this method is that you have to remember to change the fulfilment location to ensure your stock is correct at their respective locations... but I believe it would be wrong of Shopify to assume it knows where you actually fulfil the items without telling it.
So far this seems to be the way forward which allows inventory, ordering and flat rate shipping work together.
Hope this helps
I had the same problem with this issue. It was super stressful and I tried all the methods listed on this message board. The best thing I can recommend is chatting with a representative on Shopify. Rather than explaining the proper method, (the Shopify representatives are going to hate me for this, but they are much better at their job than I am) it's best to ask your Shopify representative the following question(s) ..
The key question to ask them is...
I have a customer who has numerous products in their cart from multiple (Made on Demand) locations. How do I make sure when they reach checkout that they are offered a Fixed Flat Shipping Rate that doesn't change based on the number of products (from varying MOD partners) in their cart?
Once that questions has been answered, you can work towards international shipping and free shipping rates.
Hope this helps and saves someone the time and stress of trying to figure it out on their own.