The directive states "for a period of 30 days from the day of his death." One day, from the date of his death, would be June 6, two days, from the date of his death, would be June 7, and so on. Try counting to 30 using this method and you will see that it ends on July 5, 2004, when the colors are retired for that day.
Hint: Check all flag poles at government buildings on July 4, if you're determined to plow ahead.
Very few government buildings will have anybody there on the Fourth, for me it will fly at the top at noon.