why most American slaves don't have birth record?
You cannot assume that there were none at all. It would have depended on the particular household for which a slave or many slaves worked.
http://www.google.com/search?q=slave+birth+records&rls=com.microsoft:en-us:IE-SearchBox&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7SUNA
