He was born in Yorkshire, and educated at Giggleswick School and Trinity College, Cambridge. He was the father of John Tyrwhitt, Davy Kidd who served in India for many years and Richard Bently Porson Kidd, who was rector of Potter Heigham church among other duties in Norwich, Norfolk. The last of these had a son, Richard Hayward Kidd, who was Colonial Chaplain of Hong Kong until his death in 1879.
Kidd held numerous scholastic and clerical appointments, the last being the rectory of Croxton, near Cambridge, where he died. Kidd was an intimate friend of Richard Porson and Charles Burney the younger. He contributed largely to periodicals, chiefly on classical subjects, but his reputation mainly rests upon his editions of the works of other scholars: