Hi! I can help you a little with this. I've been researching Anthony Wheelock and his family for a while.
Anthony was the eldest of four children I know of who were born to Bryan Wheelock and his wife Frances Whitney.
Anthony was born 31 December 1716, and christened 13 January 1716 (Old Style), at St. James, Westminster, Middlesex, London. He had a sister, Frances, born 04 February 1719, a brother John, born 17 February 1720, and a brother Bryan, born 01 August, 1722, but as Bryan is not mentioned in a codicil to his father's will, drawn up in 1734, that names the other three children, I suspect he died young.
Anthony's father, Bryan Wheelock, was Secretary to the Board of Trade and Plantations until his death in 1735, and Anthony himself began his career there, being appointed Clerk of the Markets in Jamaica on April 30, 1735, just after his father's death. (The post's name is a little misleading, as he wasn't actually sent to Jamaica -- he remained in London).
As to how he got to New York -- he didn't remain a clerk. Eventually he became a Captain in His Majesty's Inniskilling Regiment of Foot, which was sent to North America on May 6, 1757, during the French and Indian War.
On September 7, 1759, after the British had won a victory over the French at the battles of Fort Niagara and La Belle Famille, and had captured a few hundred prisoners, Captain Wheelock received a special commission from General Amherst, then at Crown Point, who sent him down to New York City to serve as Commissary for the prisoners of war.
Captain Wheelock was in charge of making sure the prisoners and their officers (who were placed in private homes on their parole of honour) were properly housed, paid, and kept track of, and it was also his responsibility to coordinate the prisoner exchanges arranged between the French and British.
For the next couple of years he was in close and continual contact with the captured French officers and their men. He spoke French himself, and appears to have earned the respect of both the prisoners and his own British army superiors. I've read a number of his letters and they show him to be a good and honourable man.
It took some time for all the prisoners to be finally sent back to France at the end of the war, which is why he was still in New York at the end of 1761.
Afterwards, he served as the Crown Agent for his Majesty's province of East Florida from 1770-1772, and by January 30 1779 was back in London writing his will, in which he states he is of New Palace Yard in the Parish of St. Margaret of Westminster.
In his will he leaves "to my dear wife Jane Delorest Wheelock the sum of twelve hundred pounds to purchase an Annuity for her life or to be otherwise disposed of as she pleases together with all my household furniture, plate, jewels, and every thing now in the house except my Latin and Greek books which I leave to my only son Jeffrey Wheelock." Jeffrey also gets what Anthony hopes will be an "overplus of more than two thousand pounds" after his wife gets her share, along with any and all real and personal estate. Anthony adds that, as most of his fortune consists of money due to him "from the Estates of persons dead at Jamaica and my brother John Wheelock’s (deceased) fortune is nearly in the same situation, I fear there will be considerable deficiencies in the payment of both which makes me afraid to leave Legacies to my friends where there may be no assets to pay."
His will was proved at London on 10 May 1781.
I haven't been able to find much about his son Jeffrey except for this possible mention in the Hibernian Journal, or, Chronicle of Liberty, for Monday 05 November 1781:
“From the London Gazette: War-Office, October 27 1781: 15th Regiment of Light Dragoons, Lieut. Alex Hatfield is appointed to be Captain Lieutenant, vice Lewis Majendie. Ditto Cornet Jeffrey Wheelock to be Lieutenant, vice Alex Hatfield.”
Anthony's brother John, who died in 1779, had an interesting career all his own, which you can read about here:
http://www.captaincooksociety.com/home/detail/john-wheelock-cook-s-fifth-naval-captainHope this helps fill in a few of the gaps for you. And thanks for filling in MY gaps by providing me with his wife's death date and place.