Vincent was commissioned lieutenant on 23 February 1744 and posted captain on 5 July 1748. During the summer of 1749 he commanded the Winchester 50 in the Medway.
In June 1755 he was appointed to the Dreadnought 60, recommissioning her and remaining in command for a short time before moving to the Greyhound 20 in which he served off southern Ireland.
Having joined her in the summer of 1756, Vincent took the Weymouth 60 out to the East Indies in the spring of the following year and commanded her at Vice-Admiral George Pocock’s undisciplined action with the French off Cuddalore on 29 April 1758. Unfortunately he failed to comprehend his commander’s early signals and then did not obey one for close action. Although he eventually joined the engagement, he was one of three officers subsequently brought to a court martial at Madras on 18 June, being charged with cowardice. Those of his crew who were able to write their names, some one hundred and sixty-nine men, petitioned on his behalf and declared that they were willing to face the death penalty with him. Even so, he was found partially guilty and dismissed his ship, not to serve in the Seven Years War again.
During 1766-7 he had the Glasgow in North American waters, and from 1770 until paid off in May 1771 he commanded the Hero 74, a guardship at Plymouth and Portsmouth.
In 1777 Vincent recommissioned the Yarmouth 64 and took a convoy out to Antigua in the latter part of the year. On 7 March 1778 he fell in with an American squadron off Barbados and gave chase. Closing in on the Randolph 32, Captain Nicholas Biddle, he brought her to action and a hard-fought engagement came to a rapid conclusion when his opponent suddenly exploded. All but four men rescued from the wreckage five days later were lost to his opponent, while the Yarmouth suffered casualties of five men killed and twelve wounded. On 25 July 1778 Vincent exchanged with Captain Nathaniel Batemen of the Winchelsea 32 and returned to England.
Vincent was promoted rear-admiral on 29 March 1779, vice-admiral on 29 April 1787, and admiral on 12 April 1794. He died in 1809.
He married Martha Boscawen Evelyn from Totnes, Devon, in London on 10 June 1786. She died in 1794 at Charleston, South Carolina, to which town the couple had removed, having had issue two sons.