You win the game immediately. Note that you will never be dealt both the Agent and Kingpin at the beginning of the game because of the way the cards are dealt. If you were dealt both from the beginning of the game, you'll want to ask the dealer to read the rules for dealing Integrity Cards again.
Let's say player A plays Blackmail on player B and player C to exchange one of their Integrity Cards. Before playing Blackmail, player B was the Agent and player C was the Kingpin. Player B is given an Honest card from player C and player C is given the Agent card from player B. Now player C has both the Agent and the Kingpin. Player C can flip over all their Integrity Cards and declare victory because they win the game.