Ticket to Ride trade original destination cards later in the game
You cannot trade destination cards at all: neither the ones you receive at the start nor any you receive later.

You get three at the start and can choose to keep all three or just two (discarding the other one). Rulebook:


  Shuffle the Destination Ticket cards and deal 3 cards to each player. Each player
  looks at their Destination Tickets and decides which ones they wish to keep. A player
  must keep at least two, but may keep all three if he chooses. Any returned cards are
  placed on the bottom of the Destination Ticket deck. This deck is then placed next to the
  board. Players keep their Destination Tickets secret until the end of the game.


For destination cards drawn during the game as an action, you draw three and keep one or more, discarding the one(s) you don't keep.

Again rulebook:


  – The player draws 3 Destination Tickets from the top of the deck. He must keep at least one of them, but he may keep
  two or all three if he chooses. Any returned cards are placed on the bottom of the deck.


There is no mechanism for trading them or discarding them later.