I think it needs line 686 of openfl.net.URLLoader.hx (3.4.0)to be :
this.data.position = 0;
so that when complete is called the data (as a ByteArray) is ready to be read on all platforms, as it is in the case of Flash.
The same line might be needed at line 356 as well for the case when lime_curl is not defined.
Jake