Just like bad-mouthing another person's religion, wrapping a national flag around your dog's neck, binding it up into bunting, or hanging it upside-down (an international sign of distress) are all covered by free speech. But free speech does not protect one from the scorn of others who see wrapping, binding and hanging upside-down as not showing respect for those how have sacrificed their service, even their lives, for the rights and the nation the flag stand for.
Further the post implies a belief that government (somehow separate from the citizens in the author's point-of-view) needs to respect the national symbols -- and the citizens don't -- is a strange one coming from a person stating they are a veteran