Two things here:
First, like Rich Snippets, Rich Cards aren't guaranteed even if your code is perfect. Moreover, Rich Cards were only launched globally in May 2016, and then only for recipe- and movie-related content returned in google.com.
We’re starting to show rich cards for two content categories: recipes
and movies. They will appear initially on mobile search results in
English for google.com. We’re actively experimenting with more
opportunities to provide more publishers with a rich preview of their
Second, and more pertinent to what I think you're after, Knowledge Graph is something different from Rich Snippets and Rich Cards. It's the panel at the right of search results which displays entity information, usually (but not always) derived from Wikipedia and Wikidata information.
If you're not already getting a Knowledge Graph panel for your entity, you won't get the social profile links either. The latter is contingent on the former.
Getting a Knowledge Graph result isn't always easy without having a Wikipedia article, which can mean you're subject to Wikipedia's definition of notability and the whims of its editors, but there are various articles around the web on achieving a Knowledge Graph result without a Wikipedia article.