If you go into the Origin store, either app or website, choose browse games and the rpg tab it will display all rpg games and their dlc bundles, which will allow you to purchase the dlc bundle to unlock all these in your game. For whatever reason they aren't listing the dlc bundles inside the game pages and this is causing issues.
Like Thandal said, that site is not about giving the dlc away, but instead it is to just allow people who aren't using Origin and instead still use the disk version of the game, to be able to download and install previously paid for dlc.
If you are on USA/English Origin, you should be able to use this link to see the DA2 dlc bundle: https://www.origin.com/usa/en-us/store/dragon-age/dragon-age-ii/addon/dragon-age-ii-dlc-bundle
The steps I listed above though will take you there if the link doesn't work for you in all other cases provided the languages is supported by the dlc.
There has been pretty consistent misunderstanding of that DLC page about it being free, and many people are continuing to say it is, when that is wrong. This is half on EA for the way it is posted up, and half on people for not reading that page as close as they should. They should post it up in big letters that this page is for the download and install of previously paid for legacy dlc, and all new dlc purchases should be handled through Origin....but it is what it is....