I think the EO is a pile of shit, but it doesn't purport to create a new crime. It directs law enforcement to aggressively pursue prosecutions, based on existing laws, related to flag burning.
This is what the EO says:
Sec. 2. Measures to Combat Desecration of the American Flag. (a) 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. This may include, but is not limited to, violent crimes; hate crimes, illegal discrimination against American citizens, or other violations of Americans’ civil rights; and crimes against property and the peace, as well as conspiracies and attempts to violate, and aiding and abetting others to violate, such laws.
(b) In cases where the Department of Justice or another executive department or agency (agency) determines that an instance of American Flag desecration may violate an applicable State or local law, such as open burning restrictions, disorderly conduct laws, or destruction of property laws, the agency shall refer the matter to the appropriate State or local authority for potential action.
(c) To the maximum extent permitted by the Constitution, the Attorney General shall vigorously prosecute those who violate our laws in ways that involve desecrating the American Flag, and may pursue litigation to clarify the scope of the First Amendment exceptions in this area.
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