Josias Kennington was the Reverend Kennington for St Nicholas Within during the late 1600's. Several of his children were buried in the church. According to the Alumni records of Trinity College, Dublin, Josias was the son of Thomas Kennington, who originated from Lincolnshire. I'm carrying out a surname study for Kennington, and have been looking at the Irish instances of the name - it is a very Lincolnshire-based name, although it orginated from one of 3-4 places in the South East of England in the 1300-1400s.
If you have any information regarding Rev Kennington, then please do get in touch! Thank you.