Step 1: Choose which of the PCs will be the server. In other words, which among the PCs will be your server. Your chosen PC-server will have a server application(e.g. XAMPP) installed. This PC is where you will import your existing database (.sql file). Other PCs don't have to have XAMPP(or other server applications) installed on them. Other PCs only need to have a copy of the desktop application that you created. No need to set other PCs with server application and sql.
This PC-server that you have chosen will have a connection string with localhost since I assume that all of them are not accessing the internet to use the database.
Example: jdbc:mysql://localhost:3306/yourdatabasename
Step 2: Grant privileges to the database that was setup on your chosen PC-server The simplest example is the one below.
grant all privileges on db_name.* to 'username'@'localhost' identified by 'password';
Don't forget to replace with your connections' username and password
But you may also select certain privileges based on your preference.
Step 3:
Set other PCs' connection string that has copy of the desktop application you created.
If PC-server has an IP Address of let's say 192.168.2.3 then, the connection string of other PCs will be
jdbc:mysql://192.168.2.3:3306/yourdatabasename
Other PCs will connect using the PC-Server's IP address since our database and server application was setup on PC-Server.
I hope this helps and others who might see this question.
Peace.