A quick google reveals serveral Flickr for Facebooks apps.. but I think a major value-driver for photos on FB is tagging of friends, and the "see all photos of..", "see photos of NN and me" features, and I think those are difficult/impossible to tap into without using FB's own photo app (although I don't know).
An idea could be to make an app that will upload deliberately crippled (low resolution, watermark), yet recognizable, pictures to FB, and a high-quality copy on Flickr, so tags work, but when you go the to picture, there's a note "I won't let FB own my stuff, see a high quality version of this pic on (Flickr-link) that I own. Posted by CoolPhotoApp."..
If I was on Facebook and a friend of mine started doing that, I would unfriend him for being a dick. If he tagged me in a low-res picture, so that all my friends looking for my photos would see a blurry me in the mix, I'd be pretty pissed off. Or worse: I'd ban the application, as is my prerogative, and suddenly I don't see any of these photos at all and that app destroys photos entirely.
An idea could be to make an app that will upload deliberately crippled (low resolution, watermark), yet recognizable, pictures to FB, and a high-quality copy on Flickr, so tags work, but when you go the to picture, there's a note "I won't let FB own my stuff, see a high quality version of this pic on (Flickr-link) that I own. Posted by CoolPhotoApp."..