...and, while we're here, we can add 'relative frequency' to our historical perspectives.

Burning a flag - of any nation, not only the Stars and Stripes - is a relative newcomer among symbolic actions of the type. I have a feeling it's derived from the time-honored tradition of burning effigies, but the burning of a US flag by an American is probably is no older than the anti-Vietnam War movement (and was probably copied from a protest in Vietnam, or Europe; I invite more knowledgeable people to educate me about this). As far as I know, burning someone - even the PotUS - 'in effigy' is not a crime, nor is it considered a prima facie threat against the real person. Flags, as symbols of nations, make convenient effigies. Burning one is not necessarily a threat to the nation whose flag it is.

The burning of a cross is as old as the Ku Klux Klan (that is, almost immediately post-Civil War, 137 years more or less) and means only one thing: hatred of blacks, Jews, and Catholics. It has a well-established use as a terroristic threat against individual persons.

I would draw the line here: a cross burned in a Klan ceremony is a bizarre and seemingly anti-Christian ritual, but protected "speech". A cross left burning in someone's lawn is terrorism, and should be a crime.