Who is credited with starting the "second wave" of the women's rights movement in the united states with her 1963 book the feminine mystique, and was the primary founder of the national organization for women in 1966?

Betty Friedan.

In her book, Betty Friedan argued that women in America were being misled into an unfulfilling and unhappy way of life.  They were made to believe that fulfillment and happiness as a woman came from being a wife, mother, homemaker.  But Friedan's studies of women showed that women were not happy just from that, that they were hungering for something else.  Their whole identity was coming from their roles or relationships to others in the home, not from who they actually were themselves.
Friedan was a key person among the 28 women who came together in June 1966 to found the National Organization for Women (NOW).  Today NOW has a total of 550 chapters, operating in all 50 states of the USA.