They wore red coats for one very simple reason; The King commanded it. In 1768 the King made his "Royal Cloathing Warrant" in which was he described "...the following regulations for colours and clothing, etc. of Our marching regiments of foot, to be duly observed..."
The King had His men use the colors of the "Great Union" the British flag, which were red, white and blue. There were variations between the regiments but in general all small clothes (i.e. breeches, shirt and waistcoat) were white (or occasionally buff) the coats were generally "Madder Red" with the facings and lace differing depending on the regiment. He did not pick the color to blend in as is the custom of the modern military. He picked the color to stand out and be awe-inspiring.
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