There's no official connection between Photosynth and Flickr yet or even anything like that announced. The closest thing is Creative Commons licensed Flickr photos which have already been geotagged on the map at Flickr showing up on the right place in Bing Maps Streetside and Google Maps Street View.
If there are photos on Flickr that you'd like to make a synth with, get the permission from the photographers if you're wanting to use other people's photos, download the highest quality copies to your hard drive, put them in the synther, and let it work on them. They'll be uploaded to the Photosynth servers and automatically put together as well as they can be.
If you're wanting to use your own Flickr photos, I'd have to recommend using the original copies on your hard drive, as it not only saves the time of downloading them from Flickr, but also ensures that you're not using shrunk Flickr copies that have lost detail.