I've done many backpacking trips soley for the interest to fly fish the backcountry. And I always just use standard backpacks and I try to lighten all of my load by generally using ultra lightweight gear. Pictured are two packs that I currently use on long trips. For shorter trips and/or when I really want to lighten the load I have an REI Flash backpack that holds 4000 cu. in. and is able to carry a rod case, net, and my full fishing vest. And it only weighs in at just over three pounds. IMO you don't need a fancy overpriced "fly fishing" backpack. Embrace good standard backpacking gear and you'll be better off.
This backpack is good for longer trips that don't require waders and boots. It's an REI pack sized about 4500 cu. in. and only weighs in at 4.5 pounds.
This is the beast that I use to pack waders and boots with. It's over 5,000 cu. in. but weighs six pounds.