Title 4 of the United States Code, which outlines the role of flag of the United States, specifies occasions on which all government buildings, offices, public schools, and military bases are to fly their flags at half-staff, occasions which include the deaths of presidents, vice presidents, members of Congress, justices of the Supreme Court, and state governors. As well, the President of the United States may issue proclamations directing U.S. flags to be flown at half-staff on other occasions, as was done in recent years for the death of Pope John Paul II, the interment of Frank Buckles (the last surviving American World War I veteran), the crew of the Space Shuttle Columbia's final mission (who died when the ship disintegrated during re-entry), the funeral of astronaut Neil Armstrong, and the shootings at Fort Hood, Virginia Tech, the Century Aurora theater, and Sandy Hook Elementary School.
State governors may also direct all U.S. and state flags in their jurisdictions flown at half-staff to mark the death of state officials and state residents who died on active duty as members of the armed forces. In some cases governors may also direct that flags be lowered to half-staff to honor the passing of other state residents prominent outside the areas of government and the military.
Christopher Scott "Chris" Kyle was a U.S. Navy SEAL who was known as "the Most Lethal Sniper in U.S. Military History" (a phrase which was used in the title of his autobiography). Kyle, a Texas native and resident, was shot and killed on 2 February 2013 at a Texas shooting range, and he was buried in the state capital of Austin. Texas governor Rick Perry issued a statement expressing his condolences to Chris Kyle's family "and the thousands of service members that were his extended family," but despite a good deal of public support for the gesture, Governor Perry did not issue a proclamation directing flags to be flown at half-staff statewide on the occasion of either Chris Kyle's memorial service or his funeral. (As noted above, that honor is a traditional one for those who have died while active duty members of the armed forces, but Kyle did not die on active duty, having left the U.S. Navy in 2009.)
Pop singer Whitney Houston passed away on 11 February 2012 from an accidental drowning in a bathtub, an event which the Los Angeles County coroner's office reported was due to the "effects of atherosclerotic heart disease and cocaine use." Houston, a New Jersey native, was also buried in that state, and New Jersey governor Chris Christie made a somewhat controversial decision in directing all New Jersey state flags to be flown at half-staff in her honor — critics contended that such a gesture should be reserved for members of the military, first responders, and state officials, and also that "it was wrong to honor a drug addict." Governor Christie defended his decision, saying: "I am disturbed by people who believe that because of her history of substance abuse that somehow she's forfeited the good things that she did in her life." (The previous year, Governor Christie had also directed flags to be flown at half-staff to mark the passing of Clarence Clemons, the saxophonist for Bruce Springsteen's E Street Band, with little public outcry.)
Although the White House issued a statement through press secretary Jay Carney after Whitney Houston's death noting that President Obama's "thoughts and prayers are with Whitney Houston's family, especially her daughter," as far as we know President Obama has made no public expression of condolence or mourning to mark the passing of Chris Kyle:
Example: [Collected via e-mail, February 2013]
A friend posted a meme on Facebook today, the gist of which was as follows: Chris Kyle (American soldier who was shot and killed at a gun range recently) doesn't get mentioned by Obama, but Obama had the nerve to order flags lowered to half-mast in honor of Whitney Houston.
It is not true that President Obama ordered flags throughout the country flown at half-staff to honor Whitney Houston; as noted above, that action was undertaken only at a state level by the governor of New Jersey.
In March 2016, after former First Lady Nancy Reagan died, a new version of this rumor began to circulate: specifically, that President Obama lowered White House flags for Whitney Houston, but not for Nancy Reagan. This is false, as the President called for flags at the White House and all federal buildings be flown at half-mast until her interment.