Sure, lots of pretty good fly rods can be broken down for packing. For instance, L.L. Bean makes what it calls the Travel Series fly rod, which disassembles into six pieces for a package only 22 inches in length. It's legal for carry-on luggage, plus great for strapping to a pack. I do a little fly-fishing, and haven't used this particular rod, but other Bean rods I've used feel good and are reasonably priced. The eight-foot, six-inch Travel Series rod comes in a kit with reel and leader for $269; it's $179 for the rod only. Bean also makes a nine-piece rod that breaks down to a mere 13 inches. $309 for a kit, $225 for the rod only.
Cabela's also has a bunch of rods that will work (www.cabelas.com). Their house-brand seven-piece rod (15 inches once disassembled) goes for $135, with the price rising for longer versions. You should also check out their E-Z Fold net ($13), a lightweight, quick-draw net that fits on your belt.
Finally, consider contacting Reel Deals in Albuquerque (tel: 505/268-1693), who might line you up with a high-end used rod that either comes travel-ready or can be modified in some way.