The gist of it is that apparently the Rogues were originally designed as another character’s villains, and they were intended to be colour themed.  In The Flash Companion (written by Keith Dallas and published by TwoMorrows Publishing), Carmine Infantino gave an interview about it.

“I was a fan of Captain Marvel, the original one. The reason I bring that up is because the Silver Age Flash character came from a character I created on my own, years ago, when I was trying to sell a newspaper strip. The strip was called ‘Captain Whiz and the Colors of Evil’. For me the name was a derivative of Captain Marvel who appeared in Whiz Comics. I tried to sell this to everyone. I even tried selling it to Joe Simon at Crestwood Publications. Nobody wanted it.” [snip a whole lot]

“Now all the villains you see in The Flash all came from the Colors of Evil characters I created. Every one of them. What Julie did, he gave these villains different names. So my Purple character became Gorilla Grodd. White became Captain Cold. And so on and so forth.”

[snip a whole lot]

“They were all the Colors of Evil. Captain Cold was “White”. Captain Boomerang was “Blue”.  “The Top was “Green”. Mirror Master was “Orange”. And who was the other guy? The Reverse-Flash was “Yellow”. Grodd was “Purple”. That was the only way I could handle them, by giving them colors. But Julie said “No, no. I don’t want that. I want to give them names.” I think he was right too. It makes more sense. You remember the names better.

So there are the basics of who got what colours, although I’m really not seeing Purple and Grodd.  I guess in the old-fashioned colouring of the time, he was kind of purple.

Scott Kolins once noted that he wanted to redesign the Mirror Master outfit but Geoff Johns wouldn’t let him, and in hindsight he said that was probably a good idea.  Personally, I agree — I think it’s a classic.  Infantino was an amazing designer.