How can I connect my Flutter app to local sql server database using API?

Step 1: choose a backend language/framework that will let you create a REST API. Laravel is one. If you want everything in Dart, Aqueduct I hear is a good choice.

Step 2: Make that backend do the things that need to be done with the database. Make sure you handle security/authentication. Test it with something like Postman. Manually be able to use it just like the app would use it, e.g., "making this request adds a post".

Step 3: Now develop a Flutter app that connects to this backend with a Dart package such as dio, http, etc. More info here: https://flutter.dev/docs/cookbook#networking