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Dear Ms. Arnold,
Thank you for posting your request on History Hub!
Before 1852, births were not recorded by the state of Kentucky or by any of the counties. Therefore to locate the birth records of Jacob Wainscott, we suggest searching church records in the locality where his family lived in Kentucky. FamilySearch lists several church denominations that may have records for that time period.
We searched the web and located The Historic Daniel Boone Home in Defiance, MO. According to the website, the Boone family moved from Kentucky to what became Missouri in 1799. He died there on September 26, 1820.
We hope this is helpful. Best of luck with your family research!