While “White Power” and “Black Power” may be superficially similar, both the historical context of the United States and the way each of the phrases are/have been used make them different in extremely meaningful ways.
The Confederate Flag is indeed a symbol of heritage – a dark and evil heritage.
The Confederate flag is indeed a symbol for everything for which the Confederacy stood, and the Confederacy stood for the maintenance of the institution of slavery, first and foremost.