During his service Domett was appointed as flag captain by several admirals, and saw action numerous times in this capacity, including seven years in command of HMS Royal George.

[1] The first solid record of him available was in 1769, when he joined the Navy and appears on the muster books of HMS Quebec, under the patronage of Captain Alexander Hood.

As reward for his service in this operations, Admiral John Montagu promoted Domett to lieutenant aboard HMS Romney.

On board this ship Domett saw out the war, joining Lord Howe's fleet which relieved the Great Siege of Gibraltar and later fought at the Battle of Cape Spartel.

In 1794, Lord Howe embarked on the Atlantic campaign of May 1794, which ended in the Glorious First of June, at which Domett and Royal George were heavily engaged and the ship badly damaged.

[1] At the Battle of Copenhagen, Domett disagreed with Parker's tactical plan and persuaded him to change it, resulting in the attack by Nelson at which the Danish fleet was destroyed.

On 23 April 1804, Domett was made a rear-admiral[3] but refused a seagoing commission due to a sudden deterioration of his health.

Domett was rapidly promoted during the next eight years but was unable to rejoin the fleet at sea, his health remaining too weak for the strain of such service.

[1] Instead, Domett joined the Board of Admiralty in May 1808[4] and continued to serve in an administrative capacity, his frequent bouts of ill-health making service of any kind difficult.