As luck would have it, fly-fishing and photography have fairly similar portaging needs. Mainly, lots of little compartments and places to put stuff.
Your search probably is going to begin and end with Lowepro, the company that makes more and better camera-friendly bags and packs than anyone else. At the higher end of their line you'll find the DryZone 200. It'll hold a big SLR plus four or five lenses and multiple accessories, which should give you enough space to accommodate your fishing gear, plus a camera and a lens or two. Fly boxes aren't big; I should think you could fit two or three of them into a single lens slot.
As a bonus, the DryZone is waterproof. It even floats. And that might come in handy, no? It does cost $365, however.
The other good LowePro option is the Pro Trekker 300 AW. Not totally waterproof, but highly water-resistant, and it's a little larger than the DryZone. It also has the virtue of more outside pockets and lash-on points, which makes it easier to organize a varied load such as yours. It's $300.
Mountainsmith probably is the most serious contender in this case. They make a pack called the Parallax Pro ($190) that is designed for cameras. It's similar to the DryZone in size, so can handle a camera, multiple lenses, accessories—meaning plenty of room for fly gear as well.
Happy fishing, shooting! Send us a picture of your next big brookie.