Plexamp uses BlurHash for the colours.
You can query the server for the BlurHash value for the colours.
http://IP-ADDRESS:32400/library/metadata/<ratingKey>?includeFields=thumbBlurHash,artBlurHash&X-Plex-Token=<YOUR_TOKEN>
Which will return something like
thumbBlurHash="TLCOIA=xs+}ts,S1EMI;Ne10I@j]"
artBlurHash="LmH]n4^MoIb0}pxWSNR+sRWXWrWV"
Then you decode it into the colours using the BlurHash library.