I was about to shop for the Stories DLC but I noticed I have TWoM on Steam Library and not in my GOG library, I know it's not a pricey game but I wouldn't want it to buy it twice. Does anyone know if the stories DLC (and the Little ones for that fact) can be installed into a Steam game?

You want to see what GOG Connect brings this season, I expect TWOM to be part of it as it's a great title. :D
https://www.gog.com/connect

Not sure if you can combine the two though.

Sadly it's not on GOG connect this time. TWoM is however on winter sale at the moment.
Currently the discount is a whopping 80%! :D
https://www.gog.com/game/this_war_of_mine