All I know of Henry Jones (d. bef. 28 January 1688/9) is as follows.John Jones of Philadelphia was certainly some relation, but he is not specifically described as a son of Henry Jones.
Henry Jones "of Barbados" purchases 125 acres from John Spencer in Bucks Co., Pennsylvania, in 1683.
There were a number of people named Jones in Barbados, as well as Pennsylvania. (I have made an effort to trace some of them, but without success linking any of them to the Spencers. --NMS) He is probably the Henry Jones who died in Philadelphia in 1688: Will of Henry Jones of Phila. Estate in Barbadoes and Mayamesing, Phila. Co. Wife Rachel, probably his second. Among his children is Marie, wife of William Long. Executors, John Jennings and five others all of Island of Barbadoes, and John Jones, of Philadelphia. Signed 6 mo. 19, 1688. Probated 8 mo. 16, 1688. (Philadelphia Co. Will Book A, p. 83) I will also note that, in researching Henry Jones, I found John Jennings (certainly the same who was executor of Henry Jones's estate) left a will probated in Philadelphia 28 January 1688/9, in which he names heirs (among others): his "brother" John Jones and "brother" Nathaniel Jones, as well as Samuel and Daniel Jones, sons of Henry Jones deceased. This John Jennings was also a Quaker and left a legacy to the poor of the Quakers in Barbados and Philadelphia. This John Jennings, Quaker, is probably the same who arrived in Carolina before 1679 from Barbados. John Jennings (Mariner) Commander of the ship "Joseph and Ann" was sailing between Barbados and Carolina between 1678 and 1679 (First Settlers of South Carolina 1670-1700, by Agnes Leland Baldwin). He may well be the same John Jennings found in a number of records in Barbados, Bermuda and the Carolinas.