Trump directs flags flown at half-staff for Pope Francis

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18. "upon all public buildings and ground' is modified by "of the federal government'

And does not direct anything at the state level. It's the same language used by other presidents when ordering flags to be flown at half staff. See for example:

BY THE PRESIDENT OF THE UNITED STATES OF AMERICA

A PROCLAMATION

As a mark of respect for the victims of the attack on police officers perpetrated on Sunday, July 17, 2016, in Baton Rouge, Louisiana, by the authority vested in me as President of the United States by the Constitution and the laws of the United States of America, I hereby order that the flag of the United States shall be flown at half-staff at the White House and upon all public buildings and grounds, at all military posts and naval stations, and on all naval vessels of the Federal Government in the District of Columbia and throughout the United States and its Territories and possessions until sunset, July 22, 2016. I also direct that the flag shall be flown at half-staff for the same length of time at all United States embassies, legations, consular offices, and other facilities abroad, including all military facilities and naval vessels and stations.

IN WITNESS WHEREOF, I have hereunto set my hand this eighteenth day of July, in the year of our Lord two thousand sixteen, and of the Independence of the United States of America the two hundred and forty-first.

BARACK OBAMA




https://halfstaff.org/president-obama-has-order-flags-to-half-staff-honoring-the-victims-of-the-attack-in-baton-rouge-louisiana/