Statues are offensive and must come down

That would be vandalism or destruction of private/public property. Presumably, the guy in the picture is burning his own flag, not somebody else's. So there is no crime.

Is there a guy close at hand with a fire extinguisher in case this moron accidentally sets fire to a tree?

Then yes, it is free speech.

But set fire to the Rainbow flag and see what happens...

But, however distasteful, it is free speech, provided the flag is his own.