Why do Cemeteries have flags?
Veterans are buried in normal cemeteries. The federal goverment pays for the headstones. The flag holders yare there if the families want them. Try visiting some cemeteries on Memorial Day, either observed or actual. Memorial IS a national holiday in the US.
Why do Cemeteries have flags? Because normal civilians have flags. You don't have to like it but it is a fact that previous generations honored the flag and country. With some trying to tear down our country, they taught our youth that the US was just another country and worse, that it was created by rich white slave owners or other such crap. Sadly, many young people are clueless about the real greatness of America.
Graceland is a fascinating cemetery. My husband and I have enjoyed visiting it. Many families like to commemorate a deceased loved one's military service, which they regard as part of his history and significance. One way to do it is with a small flag. On Veteran's and Memorial Days, families will sometimes visit a grave and refresh the flag while laying flowers on the grave. I'm puzzled as to why you find this odd.
That's because just about every city, town and village has veterans from military conflict. There is no requirement for a veteran to be buried in a military cemetery, and generally speaking they are filled with bodies of those who died in conflict but were brought home for burial. For vets who survive, they live out life as civilians, but proud family members want others to know of their service and sacrifices. Thus they add inscriptions to explain who the individual is and what military service was given. It's an honourable thing to have fought for one's country and flags reinforce this message.
Your headstone is given for free by the VA if you are honorably discharged and shows grade and rank.