It would probably be easiest to use one of the many API's available out there, to get the holidays for your selected county into your database. Weekends are easier because you can check the day of week with the formatDateTime function in a microflow. Store them all as calendar events in your database and add a screen where the admin can edit the holidays. Something like that?
formatDateTime($date,'EEE')='Sat' or formatDateTime($date,'EEE')='Sun'
When you are calculating SLA, check your date belongs to any holidays which is already stored in database or whether it is a weekend or not. In this way you can exclude them all in calculation.
There is a learning path with a holiday per country retrieving application doing a bit of what you need: https://academy.mendix.com/link/path/104/Logging-1
You can download the .mpk from here and use that code as a base for your module that is handling the holidays