Hi Doug:
There were Flynns/Flinns baptized in Jamaica as early as 1666. A Jane Flenn was baptized - daughter of Morrice - in 1666 in St. Andrew's, Jamaica.
Morrice and Jane Flynn baptized son William in 1680; son Samuel in 1669; daughter Anne in 1671.
Source: Jamaica, Church of England Parish Register Transcripts, 1664-1879.