finally1.js

Promise.prototype.finally = function(callback) {
  return this.then(
    function(arg) {
      function returnArg() { return arg; }
      return Promise.resolve(arg).then(callback).then(returnArg, returnArg);
    },
    function(arg) {
      function throwArg() { throw arg; }
      return Promise.resolve(arg).then(callback).then(throwArg, throwArg);
    }
  );
};

finally2.js

Promise.prototype.finally = function(callback) {
  return this.then(
    function(arg) {
      function returnArg() { return arg; }
      return Promise.resolve().then(callback).then(returnArg, returnArg);
    },
    function(arg) {
      function throwArg() { throw arg; }
      return Promise.resolve().then(callback).then(throwArg, throwArg);
    }
  );
};

rules:

• we stay either resolved/rejected with the same value
• returning a promise defer the next "next"/"catch"
• we can observe the actual value

Added a second possibility where we don't pass the arg to the finally callback, as I'm not sure it's useful.