I came across the same mistake. Given the name dart:js_util of the package which contains the function promiseToFuture(), I too thought the function should be used with a object obtained with dart:js, but is not so, and the sample in the doc is actually very clear.
The javascript Promise object must be obtained using the @JS() annotation of package:js.
Example:
@JS()
library my_lib; //Not avoid the library annotation
import 'dart:js_util';
import 'package:js/js.dart';
@JS()
external performAuthenticationInNewWindow(String uri);
performAuth(uri) async {
   var promise = performAuthenticationInNewWindow(uri.toString());
   var qs = await promiseToFuture(promise);
   print(qs);
}
Note to avoid mistake:
if a function for the interop with Javascript require an object obtained with the dart:js package, the declared type is usally not Object but JsObject or subclasses. Instead, if the object must be obtained using the @JS annotation, the declared type is Object, if it doesn't exists an appropriate external declaration
(the runtimeType of the objects obtained with the @JS annotation is NativeJavaScriptObject, but there is no corresponding class exposed in the Dart Sdk).