#Wolfram Language <s>255 213</s> 199 bytes

Fourteen bytes saved by Dennis, who avoided the " marks, using symbols instead of strings.


    SortBy[#,{yellow,green,brown,scarlet,black,ochre,peach,ruby,olive,violet,fawn,lilac,gold,chocolate,mauve,cream,crimson,silver,rose,azure,lemon,russet,grey,purple,white,pink,orange,blue}~Position~#&]&

[Try It Online!](https://tio.run/##dVLBbsIwDL3vK6wiceILJiFNO3BG4og4hOC10dK6clOqDsGvd7ZDN4a0S@Mkz6/vPad2qcLapeDdtIHX9bQjTu/jfrHaJQ5NuWtjSG@XYsQYaYCSERs4Mg0NdN5xxATH6PwnkK8YoUXnK@D@OALFcEY4B1LMh5OGGAQJJcUT@Io8RZcQatcLzDO6Wr6h7kiYQzwjA1OH4L564Y1Yyzn3XSdkImKEtuc2IgxVEJI2NKKAXVOiyOmxuN621IUUqLktlofltBUvab/ZX66Hw8vPpjA7xQoKa5KV8WRbNVg8YUW33unf7ys@Y9S43uW0Hgit6V@@rEEz0tUsaWHWjUSCyColaS2yea2yaa1yaAa/q5hNWe5a3PM1BkksH0nwBtKEc7eG/OjUJqlFHqZWNjXrnwf517a9g98klUTfh@nMz2YOR0KZvgE)