Birthdate is unlikely to be forthcoming, as there were no birth certificates at that period, and only the baptism was recorded.
Sources
"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:NPMF-R68 : 30 December 2014), John Buckingham, 06 Jun 1813; citing SAINT LAWRENCE,FOLESHILL,WARWICK,ENGLAND, reference ; FHL microfilm 559,233.
"England, Warwickshire, Parish Registers, 1535-1984," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XXG5-Q4R : 24 December 2014), John Buckingham and Charlotte Lane, 12 Oct 1834, Marriage; citing Foleshill, Warwickshire, England, Record Office, Warwick; FHL microfilm 559,235.
Acknowledgments
Internet IGI
Is John your ancestor? Please don't go away! Login to collaborate or comment, or ask our community of genealogists a question.
Sponsored Search by Ancestry.com
DNA Connections
It may be possible to confirm family relationships with John by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with John: