The single most repeated fact about the chakras outside India, that they run red, orange, yellow, green, blue, indigo and violet up the spine, is modern and can be dated closely. The Sanskrit texts assign colours, but not these: the Sat-Cakra-Nirupana gives Muladhara a red square, Svadhisthana a white crescent, Anahata a smoke-coloured hexagram, Vishuddha a white circle, and so on, and the scheme is not a spectrum. Leadbeater in 1927 gave a different set again, from his own clairvoyant claims.
The ROYGBIV rainbow arrangement now universal in popular material appears to have been introduced by Christopher Hills in Nuclear Evolution: Discovery of the Rainbow Body in 1977, and spread through the New Age publishing of the following decade. It is therefore around fifty years old. It may be a useful mnemonic; it is not ancient Indian teaching, and it should not be described as such.
Sources Rainbow Body: A History of the Western Chakra System from Blavatsky to BrennanKurt Leland with The Serpent PowerSir John Woodroffe (Arthur Avalon)