The circular patches with the "A" are the insignia of the US 3rd Army, which in WW2 was under the command of Gen. George S. Patton. The triangular tricolour patches are the insignia of the US 16th Armoured Division. If you look closely, the embroidery below the 16 shows a tank track. The 16th Armoured was established in 1943, and reached Europe in 1945. It saw combat very briefly at the end of 1945 in Czechoslovakia, before withdrawing in accordance with a treaty with the advancing Soviets.

The patch at the bottom left with the winged star is the symbol of the USAAF, which is a little confusing. Did he transfer to or from the airforce at any point?

The "16" patch is 16th Armored Division, which served in the European Theater from February to October, 1945. The triangle patch without the "16" is US Armored Force patch. The red, white, and blue "A" patch is Third Army. The red and white "A" patch is Ninth Army. The 3-color circle is the US Army Training and Doctrine Command (TRADOC), established in 1973. The patch with wings is the US Army Air Forces.

The three-color circular patch is the shoulder patch for the Army's Training and Doctrine Command (TRADOC), but during WW2 it was that of the Replacement and School Command, which was charged with the responsibility of training Army personnel. The three stripes are in the colors of, and refer to, the basic combat arms; they also refer to the components of the "One Army" concept: Active Army, Army Reserve and Army National Guard. Background The shoulder sleeve insignia was originally approved for the Replacement and School Command on 22 March 1943, and was reassigned to the U.S. Army Training and Doctrine Command on 1 July 1973. So it could very easily have been a WW2 patch in this collection. Many soldiers coming back from overseas combat were reassigned to Training and Doctrine command prior to demobilization, and some of them were used as instructors, to take advantage of their experience. The White "A" in a Cloverleaf on red is the patch for the 9th US Army, which was a major headquarters unit for the Americans during the invasion of Europe.