Kirkham Press is a name used by two separate entities:
Kirkham Press - GLBT & Erotica (2006)
This British e-publisher was new and accepting submissions for a fall anthology as of March 2006, and used to reside at kirkhampress.co.uk. However, the site disappeared in May of 2006  , and it is unknown whether any books were actually published.
Kirkham Press - Picture Books (2007-)
According to their lulu.com storefront, "Kirkham Press publishes picture books. (One) is illustrated with full-page paintings of animals. All other books have original photographs." . They are based in San Francisco.
This Press is maintained by Judy Harter and can be found at Judy Harter's Storefront on Lulu