Why is not being allowed to fly a Confederate NOT a violation of first amendment rights?

It is not illegal in any state to fly a Confederate flag.

NO ONE has said you, as a private citizen, cannot fly a Confederate flag. 

It is being suggested to halt, and in some places made illegal, to fly the flag from the public square. 

It is legal to fly the confederate flag on your own property or public property.  Just not private property whose owners do not permit it.  For example at a NASCAR race.  Not your property and not public property.  You won't be put in jail for doing so, but you will likely be escorted out the door.  Remember the US constitution only guarantees you won't go to jail for for your freedom of speech.  It doesn't not guarantee you will be free from other consequences.

Not all speech is protected by the 1st. It has restrictions and limitations. You can not just go around blathering what ever you want. You can be charged and jailed. Look it up, and watch your actions and your mouth.

Do link to the story where any legislative body has made it illegal for a private individual to fly the Stars and Bars. The removal of these things from the COMMONS, the taxpayer funded public facilities, is all anyone is asking. A person can still be as ridiculous as they want on their own private property. 

First because there is no law against flying the battle flag. (It is not a flag of the CSA) Second read the 1st Amendment: Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances. zthe Amendment only restricts action by Congress.

No law says you are not allowed to do so.  

It is a violation of them its not illegal to be racist only illegal to harm other because you're racist.

Now if hate symbols are ever deemed obcenity it will be illegal and not a violation as the first amendment doesn't cover obcenity

Because while there is a right to speak, there is no right to make other people listen, and flags and banners fall into that second category.

This is also why no one owes you a TV show, either.

And, NASCAR can decide what is allowed on THEIR property, just like Yahoo can set rules for what speech here they will allow.

Anyone can ban it on their private property, including NASCAR tracks.