The black flag indicated a dark subject matter. 

Tragedy is a genre that usually involves serious themes and high drama.  In Shakespeare's day, different flags flown over the Globe Theatre indicated different subject matter.  The black flag was used for tragedy because tragedy is “dark” and black is a dark color.  I suppose you could use red for tragedy because it involves blood, but the red flags were used for history plays.  I guess they thought that history was bloody! 

The black color is more symbolic.  It demonstrates that there is going to be a brooding subject matter.  By contrast, a white flag indicated a comedy.   A comedy is light, so it gets a white flag, and a tragedy is dark, so it gets a black flag.