Would https://community.shopify.com/c/Shopify-Discussion/No-shipping-method-available/m-p/655343/highlight... be of any use?
Most things I've just looked at suggest weights and other metrics need applying ...
Rein here from Shopify. There is some fantastic advice in this thread so I would recommend checking there first, however there are a couple of points I want to check also.
First is that you have set up shipping rates on the Shopify side of things. Even if you have a dropshipping app, you would still need to set the shipping rates to the various countries that you wish to service through the Shopify admin. There would also be an option to set global rates if you prefer.
The steps to set up flat rates are as follows:
From your Shopify admin, go to Settings > Shipping and delivery.
Next to the shipping profile* that you want to add a shipping rate to, click Manage rates.
Next to the zone that you want to add a rate to, click Add rate.
Enter the name and amount for the rate.
Optional: Add weight-based or price-based conditions.
Click Done, and then click Save.
If you want to read more about the process you can check the help page out here.
Once that is setup and your products have been added to your shipping profile you are good to go.
*Shipping profiles are ways to separate your products into groups, say for example 10 of your products have a 10$ flat rate for shipping and the remaining have free shipping. That is how you would separate your products into the groups to manage this.
You can read how to set this up here.
Any questions, feel free to ask.