Hi Justin, I'm sorry you are having trouble uploading images. Image upload was added to all our story map apps that support images a couple years ago including the Map Journal. When you click on images, just choose upload.All your images will be uploaded to the application item and have the same permissions as your app. So if you publish and only share your photos with your organization, your photos will be shared privately as well.
Hope this help. If you are still having issues, let us know.