His subsequent British commissions were: first lieutenant royal artillery, 1 Dec. 1782; brevet-major, October 1793; captain-lieutenant royal artillery, 5 Dec. 1793; brevet-lieutenant-colonel, April 1794; captain royal artillery, 9 Dec. 1796; brevet-colonel, 1 Jan. 1800.
Kœhler distinguished himself during the defence of Gibraltar in 1782 by the invention of a gun-carriage allowing the axis of the gun to be depressed to an angle of seventy degrees, the model of which is now in the royal military repository, Woolwich. The accuracy of the fire was so great that at the first trial, on 15 Feb. 1782, twenty-eight shot out of thirty fired took effect in one traverse of the Spanish San Carlos battery, at a distance of fourteen hundred yards (Drinkwater, p. 104). George Augustus Eliott, lord Heathfield [q. v.], the governor, who is said to have disliked Kœhler at first (Browne, p. 60), took him on his staff. In a letter to Sir Robert Murray Keith [q. v.], soon after the siege, Heathfield speaks of Kœhler, then at Pisa on his way to Vienna, as ‘my most confidential aide-de-camp’ (Smyth, Memoirs and Corresp. of Keith, ii. 163).
Kœhler is stated to have been at one time in Turkey, probably during the war with Austria and Russia in 1788, and to have acquired the language. He afterwards accompanied Lord Heathfield to the continent, and was with him on his way to Aix-la-Chapelle when the Flemings began their attempt to throw off the Austrian yoke. They applied for the services of a skilled artillerist, and Heathfield, through Count Dillon, recommended Kœhler, who received the rank of colonel of artillery, and afterwards of major-general in the service of the Belgian united states. He commanded the patriot troops in repeated engagements with the Austrians in 1790, in one of which, at Ardennes, 13 July 1790, he speaks of the fighting as having lasted from 3 a.m. to 7 p.m. Kœhler's reports to the ‘Sovereign Congress of the Belgian United States’ were published at Brussels in 1790. Divided counsels frustrated the Belgian attempt, and Kœhler rejoined his company of artillery at Gibraltar, and served with it at Toulon in 1793. When the place was evacuated in December 1793, Kœhler was left with two hundred men in Fort Malgere to cover the embarkation and spike the guns, a service he successfully accomplished (Duncan, ii. 67–8).
With Gilbert Elliot, afterwards first Earl of Minto [q. v.], and Lieutenant-colonel (afterwards Sir John) Moore, Kœhler was sent in 1794 to Corsica to confer with General Paoli. Lord Minto has left an amusing account of the mission (Life and Letters, 1751–1806, ii. 211 et seq.) Kœhler was quartermaster-general of the British troops at the subsequent reduction of the French garrisons in Corsica (Duncan, ii. 68), and was afterwards assistant quartermaster-general of the north-eastern district of England, with headquarters at Newcastle-on-Tyne. When the French gained a footing in Egypt in 1798, a military mission of artillery and engineer officers, with detachments of royal artillery and royal military artificers, was sent to organise the Turkish army. Kœhler was placed at its head, with the local rank of brigadier-general. The mission arrived at Constantinople in June 1799, and in January 1800 Kœhler with some of his staff, disguised as Turks, proceeded overland to Syria, returning in April. On 15 Jan. 1800 the whole party proceeded to the seat of war in Syria, arriving at Jaffa on 2 July. At the grand vizier's request plans were prepared for the defence of Jaffa. Attended by a large body of Turkish troops, the mission made a sort of royal progress towards Jerusalem. Kœhler and his men were jealously watched, but prayers were read every day in the camp without molestation. A malignant fever, produced by the filthy surroundings, carried off Kœhler's wife on 14 Dec. 1800, and Kœhler was soon afterwards attacked, and died near Jaffa 29 Dec. 1800. The remainder of the party subsequently marched with the Turkish army to join the British troops in Egypt in 1801. A narrative of the mission was subsequently published by the medical officer in charge, Dr. W. Wittman.
Kœhler died intestate. The balance of Kœhler's estate (7,842l. 8s. 4d.) was in 1814 paid over to the crown. In 1820 one Christian Bauer of Cronberg, Hesse-Nassau, labourer, and Elizabeth his wife filed a bill in the (now abolished) exchequer court at Westminster claiming Kœhler's estate as surviving next of kin. It was stated that he was the only son of George Kœhler, native of Bingen, who had enlisted in the British artillery and been killed in the service of the East India Company. After long legal inquiries it was finally decided in 1859 by Vice-chancellor Kindersley that the sum was due to his legal representatives, certain persons of the names of Kœhler and Schmidt, and after an appeal to the House of Lords in 1861 the decision was confirmed, and the original sum, together with 14,429l. 12s. 6d. interest, was restored to these claimants.