It's amazing how many people attempt to take the term "free speech" literally and avoid reading the few sentences in the actual amendment that provide context. Free speech is absolutely not the ability to say anything to anyone at any time.
Freedom of speech is a general principle and most consider it a bedrock principle of western / modern society. The US constitution provides that it won't be abridged by the government because the constitution is a document that is binding on the government of the United States. Just because it is legal to abridge someone's free speech does not necessarily make it a good idea - people are usually quite wary of platforms who place content-dependent restrictions on the type of speech that is allowed (with some notable exceptions for particularly unpopular opinions).
Note that I am not really taking a side on whether the actual theft of the flag was admirable or not here, I just want to make clear that just because it's constitutional for private individuals to do most anything (given that the constitution places almost no restrictions on individuals), that does not mean that the broader concept of freedom of speech only applies to governments.