Could his middle initials stand for Benjamin Franklin?
In the 1880 Federal Census, the "Kettle" family at Foster includes John B. F. 36, Patience C. 42, Nellie G. 13, Julia Etta 11, John B. 3, and "not named" daughter 2 mos.
The death record at Foster Town House identifies John's parents as Samuel S. & Hannah Kettell. It is not known where John & Patience's graves are.
Alden Beaman's RI Vital Record, New Series, Vol. 9, p. 34, gives his date of birth as 1843/44.