steam,origin,titanfall-2 – How to Get Titanfall 2 on Steam if Already Owned on Origin

It works one way, but not the other. You can use the keys gained in Steam (Right click on game in left-hand menu, View Game CD Key) and activate them for your EA Games account by registering them at https://activate.ea.com, which makes them then appear in your Origin games list for installation. (This applies to most - but not all - EA Games that are available on Origin)

You cannot use Origin codes to apply games to Steam, and Steam won't let you buy DLC for games you don't own though Steam.

[2015 update: You now activate them on Origin though the client. Origin menu, Redeem Product Code.]

As of the Steam Discovery Update on Sept. 23rd, 2014, Steam itself now shows you the DLC you own in the Store page without having to use browser extensions or look at the game properties in your library.

The blue markings on the left side of each DLC entry indicate that I own it already and if I hover over it, there will be a popout that shows that it's in my library.

Note that isn't perfect. In this particular example, Steam shows that I don't own Wonders of the Ancient World, even though I do, but I'm guessing that's a problem with that particular piece of DLC, as it's done that since release. However, Steam still won't let you buy anything you already own, so you're safe from double purchases.