You will have to ask Obama. Perhaps he wanted to start the honor on the same day he spoke about it to veterans at the VFW convention in Pittsburg, Tuesday.
"We draw strength from yet another American community that has come together with an unmistakable message to those who will try to do us harm: We will not give in to fear, you cannot divide Americans, you can never change our way of life or the values of freedom and diversity that make us Americans," Obama said.
"We honor our five service members killed so senselessly in Chattanooga," he said. "We are grateful to the courageous police who stopped the rampage and saved lives."
The president has been quick to order the flag lowered after similar tragedies, issuing a proclamation the same day of the 2012 attacks in Benghazi and after 12 were killed at the Washington D.C. Navy Yard. And it was lowered just one day following the Boston Marathon bombings and the Fort Hood shootings.