This is the design of the plugin itself. It's designed to only show one gallery per page.

To allow additional galleries to be displayed, a custom code can be added to each gallery. To add the code:
  1. Navigate to Flickr Album Gallery
  2. Hover over the gallery which you want to display and click Edit
  3. On the right hand side, note the new Gallery ID, in the screenshot example below it’s 1192User-added image
  4. Copy the following code:
  5. .galleryXXXXX {
        overflow: inherit !important;
    }
  6. Paste the Code into the Custom Css section of the Gallery
  7. Replace the XXXX with your new Gallery ID
  8. Click Update