Peggy Flanagan has won the Democratic nomination for the U.S. Senate in Minnesota. Peggy Flanagan has won the Democratic nomination for Minnesota's U.S. Senate seat, beating out Rep. Angie Craig. Peggy Flanagan wins DFL nomination for US senateBig picture view:Flanagan has won the Democratic nomination for one of Minnesota’s U.S. Senate seats. This seat in the Senate for Minnesota opened because Democrat Sen. Tina Smith (D) announced she was not running for re-election. Peggy Flanagan?