The item in the /Roster of Soldiers/ volume that you cite is for a pay voucher issued to an Ambrose McKee of Salisbury Dist.
It is #3451 listed in the book.It does not give a birth date or place.
The birth date was invented as an estimate by the Godfrey Memorial Library, which compiled the AGBI.The birth-place is similarly an estimate by Godfrey Memorial Library, compiler of the AGBI.Many moved to NC from elsewhere before the Revolutionary War.The Godfrey Library estimates could be wrong on both counts.
The Vol. 14 is of the AGBI, not the DAR compilation.
You can request a copy of the NC-DAR book page from the DAR Library.This web site has instructions for doing so, and a form you can print out for requesting the copy.