It's true that many people with flat feet find more comfort in a wider shoe, one that doesn't pinch in the arch area. So Plan A would be to find a wider boot. You'll really need to visit a good snowboard shop and talk to a boot fitter to get the best fit (and I'm surprised someone even sold you the Burtons, given your condition). And even at that, things will be a little tricky, as you want the boots to feel a little tight when you buy them, as the inner lining will compress after use, easing the fit.
Anyway, here are some good candidates: The Airwalk Freeride ($160) may work well for you because it has heat-moldable insoles, so you can custom-fit the boot to your foot. K2's Tracker Boa boot ($229; www.k2snowboards.com) uses cables and a knob system, rather than laces, to tighten the boots, a setup that gives you good control over the fit. And, Van's BFB boots ($189; www.vanssnow.com) have insoles that, like those on the Airwalks, can be heat-molded to fit your feet.
With all that, once you have the boots in hand you still may want to see a foot specialist to see if a custom orthotic would make you more comfortable on your powder days.