In December, a half-dozen of some of the richest families in the U.S., from agriculture to beverages, gathered in a conference room on the 10th floor of an office building in Miami. This was not some cabal to rule the world. Instead, for an hour over coffee and bagels they listened to a dealmaker for billionaire brothers J.B. and Tony Pritzker talk about how to buy companies. Wealthy families are embracing their inner Warren Buffett, albeit on a smaller scale. They used to hand most of their assets to managers to invest. Now, following the likes of Buffett, Michael Dell...