It's not an ending. Renk is the word for colour, and here what has happened is renk+a+renk, with consonant mutation making the final letter in the first renk into a "g" (compare renk + accusative suffix -i = rengi etc.).
According to the Nişanyan Sözlük, rengarenk was first used by Evliya Çelebi in his Seyahatname (1680) and means the same thing as renk renk. Repeating a word like this expresses intensity in Turkish, e.g. sık sık = very often, çok çok = very much, so if renk = colour, then renk renk = lots of colour, i.e. colourful.
Hmmm, according to the TDK, "rengârenk" is actually a Farsi loanword (and the pronunciation would suggest this as well). A native Farsi speaker on Duolingo has also said that the same phrase in Farsi is "rengo va reng," suggesting that this was brought over from a perceived pronunciation by Turks of this phrase.
To the best of my knowledge, there is no other word like this in Turkish, as the more native Turkish way to do this is just to repeat the word (which would be 'renk renk' as you said) :)
My point was not that the word itself was Arabic, but that the practice of repeating words - such as "renk renk" - is one that is also used in Arabic. This could be a coincidence, but given the influence Arabic has had on other languages in the Middle East (both Turkish and Farsi), it might well not be.