"What are the laws regarding flying a Confederate Flag on private property?"
*** Though there were several 'Confederate flags', I assume you are referring to the 'Confederate Battle Flag' and/or the 'Confederate Navy Jack'. They are similar. If you want to know more about the REAL history behind the flags of the Confederacy, go to:
http://www.confederateflags.org/
And back to your original question, there aren't any laws that would restrict your 'right to free speech' as to displaying the 'Flag of the Confederacy'. However, if that flag is going to be displayed with a US flag, the rules of display in the US Code (4 USC 1, et seq) should be followed. They are at:
http://www4.law.cornell.edu/uscode/4/ch1.html
More on the US flag can be found at:
http://www.homeofheroes.com/hallofheroes/1st_floor/flag/1bfb_disp1.html