I would assume he is buried in the Confederate Cemetery there in Jackson, Mississippi.

Hi Tim, I was not able to fine his resting place, the Researchers here gave me this Cemetery link,
Greenwood Cemetery

http://upload.wikimedia.org/wikipedia/commons/4/41/GreenwoodCemetery.jpg

His son is an great uncle of mine, can I still order William C Grizzle Militery Record ?

even if he is not a kin folk ?