I am trying to get the Downloads folder on my dock in the Fan view, as seen in this picture:
However, when I click on the folder, the folder immediately opens instead.
Find the download folder you added to the dock. Right click on that folder and do get info. In the pane that opens there should be a line that says "Original" with the location of the actual downloadeds folder. Go to that downloads folder and drag it to the dock area where the other download folder is located. Remove that first download folder from the dock and place this new download folder there instead. Now you should be able to set it up as a fan.