#Wolfram Language 255 213 199 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~#&]&

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Wolfram Language 255 213 199 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~#&]&

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#Wolfram Language 255 186 bytes

There should be a way to efficiently compress the list of colors.

SortBy[#,StringSplit@{"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~#&]&

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#Wolfram Language 255 213 199 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~#&]&

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#Wolfram Language 255 186 bytes

There should be a way to efficiently compress the list of colors.

SortBy[#,StringSplit@{"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~#&]&

#Wolfram Language 255 186 bytes

There should be a way to efficiently compress the list of colors.

SortBy[#,StringSplit@{"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~#&]&

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