Flat rate shipping is allowing only one location/region to be set.
This sounds like you need rule based shipping.
Unfortunately, AbanteCart does not have this yet. We can think of developing one for you and others.
I afraid there is no clean easy way to do this, only work around.
Not sure if you like this but it will work and easy to set:
1. Use weight based shipping extension Extensions -> Shipping
2. Set locations (countries) you need System -> Localization -> Locations
3. Set 1 rate cost per each location in Weight Based Shipping -> Additional settings
This will give you fixed cost per location (country in your case).