Don't even need to 'distribute' the wealth[1]. Just burn it. It's the inequality itself that causes problems--out-of-touch billionaires having the power to make the rest of us do their bidding, whether it makes any dang sense or not--not the lack of giant wads of dollar bills in everybody's pockets.

[1] If by 'wealth' we mean numbers in computers. Actual wealth, like healthy land and clean water and manufacturing capacity should be shared by everyone, but currently money is what controls it.