How do I call a super constructor in Dart?

Can I call a private constructor of the superclass?

Yes, but only if the superclass and the subclass you are creating are in the same library. (Since private identifiers are visible across the whole library they are defined in). Private identifiers are those that start with underscore.

class Foo {    
  Foo._private(int a, int b) {
    //Code of private named constructor
  }
}

class Bar extends Foo {
  Bar(int a, int b) : super._private(a,b);
}

Yes, it is, the syntax is close to C#, here is an example with both default constructor and named constructor:

class Foo {
  Foo(int a, int b) {
    //Code of constructor
  }

  Foo.named(int c, int d) {
    //Code of named constructor
  }
}

class Bar extends Foo {
  Bar(int a, int b) : super(a, b);
}

class Baz extends Foo {
  Baz(int c, int d) : super.named(c, d);  
}

If you want to initialize instance variables in the subclass, the super() call must be last in an initializer list.

class CBar extends Foo {
  int c;

  CBar(int a, int b, int cParam) :
    c = cParam,
    super(a, b);
}

You can read about the motivation behind this super() call guideline on /r/dartlang.

This is a file I am sharing with you, run it as is. You'll learn how to call super constructor, and how to call super parameterized constructor.

// Objectives
// 1. Inheritance with Default Constructor and Parameterised Constructor
// 2. Inheritance with Named Constructor

void main() {
    var dog1 = Dog("Labrador", "Black");
    var dog2 = Dog("Pug", "Brown");
    var dog3 = Dog.myNamedConstructor("German Shepherd", "Black-Brown");
}

class Animal {
    String color;

    Animal(String color) {
        this.color = color;
        print("Animal class constructor");
    }

    Animal.myAnimalNamedConstrctor(String color) {
        print("Animal class named constructor");
    }
}

class Dog extends Animal {
    String breed;

    Dog(String breed, String color) : super(color) {
        this.breed = breed;
        print("Dog class constructor");
    }

    Dog.myNamedConstructor(String breed, String color) : super.myAnimalNamedConstrctor(color) {
        this.breed = breed;
        print("Dog class Named Constructor");
    }
}

case of a constructor with Optional Parameters

class Foo {
  String a;
  int b;
  Foo({this.a, this.b});
}

class Bar extends Foo {
  Bar({a,b}) : super(a:a, b:b);
}