That target you refer to is called a roundel.

The first use of a roundel on military aircraft was during the First World War by the French Air Service. The chosen design was the French national cockade, which consisted of a blue-white-red emblem mirroring the colours of the Flag of France. Similar national cockades were designed and adopted for use as aircraft roundels by their allies. The British Royal Flying Corps (RFC) abandoned their original painted Union Flags because they looked too much like the German cross and the British soldiers in the trenches had shot at them mistaking them for German aircraft. Instead, British aircraft roundels were eventually designed to use the French colours in reverse, red-white-blue from centre to rim, after a short period of using a red-rimmed white circle that closely resembled the roundel, used to this day, by Denmark. This red-white-blue from center to rim roundel design was subsequently adopted by British Imperial air forces with a maple leaf (RCAF), kangaroo (RAAF), and kiwi (RNZAF). During WWI, roundels based on national cockade colours were subsequently adopted by the air forces of other countries, including the U.S. Army Air Service.

Luftwaffe established in 1935 under Göring, in contravention of the Treaty of Versailles.

The forerunner of the Luftwaffe, the Imperial German Army Air Service (Luftstreitkräfte), was founded in 1910 with the emergence of military aircraft. After the First World War ended in German defeat, the Luftstreitkräfte was dissolved completely under the conditions of the Treaty of Versailles, which demanded that its aeroplanes be completely destroyed.

During WWI the aircraft were under the command of the US Army Air Corps.

After WWII, the US Air Force was created.

The French Air Force was originally founded in 1910 and was called Armée de l’Air, and Britain’s Royal Flying Corps (which merged in 1918 with the Royal Naval Air Service to form the Royal Air Force), was founded in 1912.

The first use of a roundel on military aircraft was during the First World War by the French Air Service. The chosen design was the French national cockade, which consisted of a blue-white-red emblem mirroring the colours of the Flag of France. Similar national cockades were designed and adopted for use as aircraft roundels by their allies. The British Royal Flying Corps (RFC) abandoned their original painted Union Flags because they looked too much like the German cross and the British soldiers in the trenches had shot at them mistaking them for German aircraft. Instead, British aircraft roundels were eventually designed to use the French colours in reverse, red-white-blue from center to rim, after a short period of using a red-rimmed white circle that closely resembled the roundel, used to this day, by Denmark. This red-white-blue from center to rim roundel design was subsequently adopted by British Imperial air forces with a maple leaf (RCAF), kangaroo (RAAF), and kiwi (RNZAF). During WWI, roundels based on national cockade colours were subsequently adopted by the air forces of other countries, including the U.S. Army Air Service, which would later become the US Air Force and would use a star with stripes on each side for its emblem.

Both the US Navy and the US Army had airplanes. It wasn’t until 1947 that the US Air Force was created. The UKGBNI had Her Majesty’s Royal Air Force.

The Soviet Air Force

The Royal Air Force (RAF)

Army Air Coprs (later US Air Force)

RCAF, RNZAF, RAAF