I think most of the family fortune came not from bootlegging, but from manipulation on Wall Street, which would qualify as "insider trading" under today's regulations, if not those in force then.
Joe was as much a mobster as any Sicilian.
The Crash
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Kennedy formed alliances with several other Irish-Catholic money men, including Charles E. Mitchell, Michael J. Meehan and Bernard Smith. He helped establish the Libby-Owens-Ford stock pool, an arrangement in which Kennedy and colleagues created an artificial scarcity of Libby-Owens-Ford stock to drive up the value of their own holdings in the stock. Using inside information, and the public's lack of knowledge, a pool operator would bribe journalists to present that information in the most advantageous manner. The stocks would then change in price up or down depending on the position favoured by the pool.
Kennedy got out of the market in 1928, long before the Crash, locking in multi-million dollar profits. Indeed when the 1929 crash did come, he made money due to his short positions.
http://en.wikipedia.org/wiki/Joseph_P._Kennedy,_Sr.