Clinton's comments came at a church just 6km from Ferguson, Missouri, where unarmed black teenager Michael Brown was shot dead by a white police officer in August, sparking weeks of protests and a national debate about race relations.
The Emanuel bloodbath has prompted smaller demonstrations, with some, including Governor Nikki Haley, calling for the Confederate flag at the state legislature in South Carolina's capital Columbia to be removed.
Clinton said she supported Haley's calls, and said the flag was a "symbol of our nation's racist past that has no place in our nation's present or future."
"It shouldn't fly there, it shouldn't fly anywhere."
Clinton, a former US secretary of state and ex-senator, has called for tougher gun laws in the wake of the latest tragedy.