It is not possible to watermark Flickr images using Juicebox. Only local images can be watermarked by JuiceboxBuilder-Pro.
Watermarking is a feature of JuiceboxBuilder-Pro (the application used to build Juicebox-Pro galleries) rather than Juicebox-Pro itself.
The watermarks are not applied to the images by Juicebox-Pro at the time the images are displayed in the gallery. The watermarks are baked into the images (by JuiceboxBuilder-Pro) at the time they are resized when the gallery is created.
As JuiceboxBuilder-Pro does not process Flickr images when a gallery is created, the Flickr images cannot be watermarked.

You would need to add watermarks to your images (perhaps using JuiceboxBuilder-Pro or an imaging program such as Adobe Photoshop), upload the watermarked images to Flickr and then display them in your gallery using the available Flickr configuration options.