Some sites allow photo uploads with a URL address. If yours does you can upload the photo to one of those sites first, and used a link to that file. Unfortunately it requires a full link, ending in the file's name and extension. Few sites still generate this type of link, preferring secure or shortened links that end in some sort of text hash.
Dropbox can generate the right kind of link, but the file must be in the public directory, and you have to generate the link from their site. The app only creates shortened links, though you can use it to upload the photos to the DropBox public folder.
Flickr won't give you the direct link, directly. However if you ask it to generate embedded code you can copy the needed link out of the result. It begins with http: and ends with the file's name. You can only do this from their site. You can use the app FlickrStacker to upload photos to it.
You take that code and paste it into the URL upload option on your site, if it has one.
I'm sure there are other cloud storage and sharing sites that will do the same, but those are the only two I'm sure of.