You can email photos to a flickr or photobucket acct if you check in your acct details section, they will give you an email and if you send them to that email they upload it to your account. Check on facebook mobile.....they might have the same feature, its been awhile since I checked it out.
its' a shame that we can't have file access on the iPhone. Every other smartphone I've had, I've been able to upload a pic or file directly to a website that I'm on. I put things on craigslist to sell all the time and am able to directly upload photos from my N95.
Try iPhoneslide.com. You just send an email to them with pic attached, and you get a mail back with a link, you follow link and tell it where you want the photo to go - it supports Facebook, Flickr, Twitter, and some blogging platforms. No registration required.
For just Flickr, there's also iFlickr (native app) to snap and send one pic at a time straight to Flickr ...