When do I get it? I've downloaded and installed the DLC but I don't know when im suppose to get it.

Yeah I unlocked, downloaded and installed the DLC as well including the troll quest but the Jacket does not show up in my game.

People say it's there when they play the prologue, but I'm still wearing the default leather jacket.

It should be in your inventory right from the beginning (or at any given time, as soon as you install the DLC).
If it is not, check if your game is registered correctly (start retgister.exe from the game folder and make sure you entered your key with CAPITAL letters only). If it is, it's most likely a server-side (or at least CDP-side) problem and should be fixed with the upcoming patch.