No, the application won't work with the new Photos app. This matter has been discussed on the developer's forums. Users have issues with Shutterfly Express Uploader not being able to work with the Photos app. However, you will have to manually get the images out of iPhone and then use the uploader to send them to Shutterfly. To do this, open Spotlight and type iPhoto. Although it has been replaced, the application is still available. Once opened, go to File > Export. This will get out photos from iPhone area.
This is the only fix available for this situation.