This John would not have been a direct descendent of Admiral Sir Jahleel Brenton as he had two sons and two daughters. The eldest son died as a teenager in England, and the other son died without having children. Both daughters married and children.
This John would not have been a direct descendent through the Admiral's father, who was also Rear Admiral Jahleel Brenton. He had three sons, Jahleel (above) and Edward Pelham who had no children of his own, and James, who died during a naval battle while on board the Petrel.
I do however, believe he is related, as many of Rear Admiral Jahleel Brenton's siblings and nephews also reamained with the British Navy.
I just don't know which one yours belongs to yet.