Karen Finney's exact age is not found online at this time. However, based on her experience in politics and other biographical information on her, she is likely in her late 30s or early 40s. She worked on Bill Clinton's 1992 presidential campaign.
If you think about it, many people who work in politics/government go to college before getting a steady job. Some have internships while in college, but this is usually in their later years of college. Several recent biographies state that she has 16 years of experience in politics. In addition, based on observation of pictures and videos of her, it appears that this is a reasonable estimate.
Karen Finney became well known by many when she was Deputy Press Secretary for Hillary Clinton in the 1990s. She's an independent political consultant/analyst, who has worked for MSNBC, New York State, the Clinton Administration, and the Democratic National Committee.
In the video below, Karen Finney recently discussed the Romney campaign with Rachel Maddow: