There is absolutely no question regarding the Constitutional First Amendment protection regarding the burning of the American flag.  Mr. Trump's comments provide some more "red meat" for his supporters, but they have no foundation in law.  In fact, historically the method for disposing of a "desecrated" or, perhaps, just warn out, American flag is to burn it in private.  So, clearly the "burning" is not in question.  The real issue is burning the flag as a protest against actions by the American government...and, that, is clearly established as a protected exercise of freedom of expression.  

If Mr. Trump would like to propose a Constitutional Amendment to exempt "flag burning" from the "First Amendment Rights", he is, of course, free to do so.