The singleton example shows how to do this (substitute your singleton class name for Immortal). Use a factory constructor to implement the singleton pattern, as shown in the following code:

class Immortal {
  static final Immortal theOne = new Immortal._internal('Connor MacLeod'),
  String name;
  factory Immortal(name) => theOne;
  // private, named constructor
  Immortal._internal(this.name); }

main() {
  var im1 = new Immortal('Juan Ramirez'),
  var im2 = new Immortal('The Kurgan'),
  print(im1.name);               // Connor MacLeod
  print(im2.name);               // Connor MacLeod
  print(Immortal.theOne.name);   // Connor MacLeod
  assert(identical(im1, im2));
}

All Immortal instances are the same object.

The Immortal class contains an object of its own type, which instantiates itself by calling the private _internal constructor. Because it will be unique, we declare it as static. The factory constructor always returns this instance; only one instance of the Singleton class (named Immortal here) can ever exist in the executing isolate. It has to be a factory constructor because only this type can return a value. The code can even be shortened, shown as follows:

class Singleton {
  factory Singleton() => const Singleton._internal_();
  const Singleton._internal_();
}