I think a modern U.S. Civil War will look a lot like Syria. Once social order collapses, you'll get a bunch of different armed factions all pursuing their own social agenda. Remember that the 99% generally hates each other a lot more than they hate the rich; I can't imagine a Nazi from North Carolina, an Evangelical from Arkansas, a proud Southerner from Alabama, a blue-collar Irish Catholic from Boston, a cattle-rancher from Montana, a Jewish doctor from NYC, a poor urban black from Atlanta, and a Californian tech-worker all fighting on the same side.
Any conflict where the U.S. disintegrates will likely spread worldwide, too, as other nations take advantage of the power vacuum to press their own claims. So emigration is unlikely to be a solution for people who wish to remain neutral.
The endgame for the 1% is likely to become lords or petty kings of little feudal domains. They may offer to provide security services to their employees in exchange for economic service. They wouldn't be global titans of industry, but they'd be heads of their little fiefdoms. The smart ones will avoid major military action, instead only clearing the local area around their corporate offices of populist insurgents. If the insurgents want to fight other insurgent groups, that's their business; they can all kill each other off.