Использовать FileStream.
Код AS3:
var fileLocal:File = File.applicationStorageDirectory.resolvePath(pathLocal);
var fileStream:FileStream = new FileStream();
fileStream.addEventListener(Event.CLOSE, fileClosed);
fileStream.openAsync(fileLocal, FileMode.WRITE);
fileStream.writeBytes(fileData, 0, fileData.length);
fileStream.close();