I recently made email contact with a man who is very knowledgeable about Barbados genealogy.I haven't yet made sense of all this information so I'm just going to paste it in this post and you can see what you make of it.
"I started by looking in my Barbados genealogy reference library here in California for who the first Walke males were on Barbados in the early half oh the 1600s, and to see if there was a Thomas Walke among them. That led me to a Robert Walke being the first recorded Walke on Barbados. There was no birth/baptism record found on Barbados for Robert Walke so it is probable that he had come from England as a younger man. I searched the English records and found the record for only one Robert Walke so I have to assume (dangerous) this is the right one. Robert Walke was baptised on 29 Apr 1629 in Holbeton, Devon, England, and his father's name was Walter Walke. No mother's name shown. I searched in the ship's passenger lists for emigrants from England to Barbados in that early time period (first settlers of Barbados came from England starting in about 1627) but found no Robert Walke listed. I did find a Robert Walkin who had gone to Virginia prior to 1624 and who died in 1624 in Virginia but this obviously was not the right dude. I found the Will for Robert Walke (in Barbados St. Thomas Parish Register RB6/12, page 377, dated 30 Aug 1682) and in that Will, it identifies Robert Walke's wife being named Anne (no marriage record found anywhere for their marriage so I don't know her maiden name) and identifies his 6 children shown next. I am going to assume (dangerous) that he named his children starting with the oldest first as was common in Wills. There are no ages shown, but I'll give you a tentative estimate of birth year based on the father Robert having been born in 1629, and getting married probably at about age 28 (in circa1657) in Barbados: 1) Robert Walke (Jr.), and this fits the Barbados custom of naming the first born son after his father. Born circa 1660. 2) Thomas Walke, born circa 1662. (The record shows his death to have been 1694, but probably was later than that.) 3) John Walke, born circa 1664. 4) Jonathan Walke, born circa 1666. I later found a baptism record for a Jane Walke, daughter of Jonathan and Mary Walke, baptised in St. Michael on 18 Feb 1691. I also found a baptism record for a Mary Walk daughter of Jonathan Walk baptised in St. Michael on 15 Sep 1692 so this is about the right year of birth for their father Jonathan. I spaced my estimates of the earlier and later births of Jonathan's siblings to be about 2 years apart centered on Jonathan's birth year of 1666. 5) Margery Walke, born circa 1668. 6) Mary Walke, born circa 1670.
More about Robert Walke. I found in the Barbados Census of 1679, which includes everyone on the island of Barbados (plantation owners, servants, men serving in the Barbados Militia, British Army personnel, etc. that Robert Walke (then about age 50) was an officer in the Barbados Militia under the command of a Lt. Col. James Carter in 1679. Robert Walke is listed on the militia role as being a "cornet", which according to my dictionary was the British name for an officer who carries the flag (colors) for a troop of Cavalry. Elsewhere in that Census of 1679, it shows this Robert Walke Sr. as owning 20 acres of land in St. Thomas Parish on Barbados (probably named his plantation "Walke's Springs", which I found in another reference "Genealogy of Barbados Families"). Robert Walke's Will was proved 29 Aug 1683 so he had died sometime between Aug 1682 and Aug 1683.
You commented something about a Sir Thomas being given land on Barbados out of loyalty to Charles II? What I have seen in the records doesn't indicate that, but it does indicate that his father Robert Walke owned 20 acres of land in St. Thomas, and this could very well indicate that Robert Walke had been given those 20 acres out of loyalty. Whether he was a Sir Robert, I don't know. But he was an officer in the Barbados Militia, and officer rank frequently was awarded by the British Government to those plantation owners on Barbados who held more than 15 acres of land on Barbados."
I hope this helps.I am descended from William Walke and Mary Calvert. If I understood your other posts correctly, they are our most recent common ancestors.