dart advantage of a factory constructor identifier

A normal constructor always returns a new instance of the current class (except when the constructor throws an exception).

A factory constructor is quite similar to a static method with the differences that it

can only return an instance of the current class or one of its subclasses
can be invoked with new but that is now less relevant since new became optional.
has no initializer list (no : super())

So a factory constructor can be used

to create instances of subclasses (for example depending on the passed parameter
to return a cached instance instead of a new one
to prepare calculated values to forward them as parameters to a normal constructor so that final fields can be initialized with them. This is often used to work around limitations of what can be done in an initializer list of a normal constructor (like error handling).

In your example this code

  studentId: parsedJson['id'],
  studentName : parsedJson['name'],
  studentScores : parsedJson ['score']

could be moved to the body of a normal constructor because no final fields need to be initialized.