"Notwithstanding the Supreme Court’s rulings on First Amendment protections, the Court has never held that American Flag desecration conducted in a manner that is likely to incite imminent lawless action..."

"... or that is an action amounting to 'fighting words' is constitutionally protected. See Texas v. Johnson, 491 U.S. 397, 408-10 (1989). My Administration will act to restore respect and sanctity to the American Flag and prosecute those who incite violence or otherwise violate our laws while desecrating this symbol of our country, to the fullest extent permissible under any available authority.... The Attorney General shall prioritize the enforcement to the fullest extent possible of our Nation’s criminal and civil laws against acts of American Flag desecration that violate applicable, content-neutral laws, while causing harm unrelated to expression, consistent with the First Amendment...."

From President Trump's executive order, "Prosecuting Burning of the American Flag."

Does that violate the First Amendment even though it explicitly limits itself to what is "consistent with the First Amendment"?

Here's Texas v. Johnson. 

I feel like rereading the dissent:

As the Court analyzes this case, it presents the question whether the State of Texas, or indeed the Federal Government, has the power to prohibit the public desecration of the American flag. The question is unique. In my judgment, rules that apply to a host of other symbols, such as state flags, armbands, or various privately promoted emblems of political or commercial identity, are not necessarily controlling. Even if flagburning could be considered just another species of symbolic speech under the logical application of the rules that the Court has developed in its interpretation of the First Amendment in other contexts, this case has an intangible dimension that makes those rules inapplicable.

A country's flag is a symbol of more than "nationhood and national unity."... It also signifies the ideas that characterize the society that has chosen that emblem as well as the special history that has animated the growth and power of those ideas. The fleurs-de-lis and the tricolor both symbolized "nationhood and national unity," but they had vastly different meanings. The message conveyed by some flags -- the swastika, for example -- may survive long after it has outlived its usefulness as a symbol of regimented unity in a particular nation.

So it is with the American flag. It is more than a proud symbol of the courage, the determination, and the gifts of nature that transformed fledgling Colonies into a world power. It is a symbol of freedom, of equal opportunity, of religious tolerance, and of goodwill for other peoples who share our aspirations. The symbol carries its message to dissidents both at home and abroad who may have no interest at all in our national unity or survival.

The value of the flag as a symbol cannot be measured. Even so, I have no doubt that the interest in preserving that value for the future is both significant and legitimate. Conceivably, that value will be enhanced by the Court's conclusion that our national commitment to free expression is so strong that even the United States, as ultimate guarantor of that freedom, is without power to prohibit the desecration of its unique symbol. But I am unpersuaded. The creation of a federal right to post bulletin boards and graffiti on the Washington Monument might enlarge the market for free expression, but at a cost I would not pay. Similarly, in my considered judgment, sanctioning the public desecration of the flag will tarnish its value -- both for those who cherish the ideas for which it waves and for those who desire to don the robes of martyrdom by burning it. That tarnish is not justified by the trivial burden on free expression occasioned by requiring that an available, alternative mode of expression -- including uttering words critical of the flag, see Street v. New York, 394 U. S. 576 (1969) -- be employed.

It is appropriate to emphasize certain propositions that are not implicated by this case. The statutory prohibition of flag desecration does not

"prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion or force citizens to confess by word or act their faith therein."

West Virginia Board of Education v. Barnette, 319 U. S. 624, 319 U. S. 642 (1943). The statute does not compel any conduct or any profession of respect for any idea or any symbol.

Nor does the statute violate "the government's paramount obligation of neutrality in its regulation of protected communication." Young v. American Mini Theatres, Inc., 427 U. S. 50, 427 U. S. 70 (1976) (plurality opinion). The content of respondent's message has no relevance whatsoever to the case. The concept of "desecration" does not turn on the substance of the message the actor intends to convey, but rather on whether those who view the act will take serious offense. Accordingly, one intending to convey a message of respect for the flag by burning it in a public square might nonetheless be guilty of desecration if he knows that others -- perhaps simply because they misperceive the intended message -- will be seriously offended. Indeed, even if the actor knows that all possible witnesses will understand that he intends to send a message of respect, he might still be guilty of desecration if he also knows that this understanding does not lessen the offense taken by some of those witnesses. Thus, this is not a case in which the fact that "it is the speaker's opinion that gives offense" provides a special "reason for according it constitutional protection," FCC v. Pacifica Foundation, 438 U. S. 726, 438 U. S. 745 (1978) (plurality opinion). The case has nothing to do with "disagreeable ideas," see ante at 491 U. S. 409. It involves disagreeable conduct that, in my opinion, diminishes the value of an important national asset.

The Court is therefore quite wrong in blandly asserting that respondent

"was prosecuted for his expression of dissatisfaction with the policies of this country, expression situated at the core of our First Amendment values." 

Ante at 491 U. S. 411. Respondent was prosecuted because of the method he chose to express his dissatisfaction with those policies. Had he chosen to spraypaint -- or perhaps convey with a motion picture projector -- his message of dissatisfaction on the facade of the Lincoln Memorial, there would be no question about the power of the Government to prohibit his means of expression. The prohibition would be supported by the legitimate interest in preserving the quality of an important 

national asset. Though the asset at stake in this case is intangible, given its unique value, the same interest supports a prohibition on the desecration of the American flag.

The ideas of liberty and equality have been an irresistible force in motivating leaders like Patrick Henry, Susan B. Anthony, and Abraham Lincoln, schoolteachers like Nathan Hale and Booker T. Washington, the Philippine Scouts who fought at Bataan, and the soldiers who scaled the bluff at Omaha Beach. If those ideas are worth fighting for -- and our history demonstrates that they are -- it cannot be true that the flag that uniquely symbolizes their power is not itself worthy of protection from unnecessary desecration. 

Who wrote that? Not Scalia. He joined the majority and he was wont to use it as an example of how his method of interpretation got him to some results he didn't like.

No, that Texas v. Johnson dissent was written by Justice John Paul Stevens.