You cannot query whether a specific value exists in a list. This is one of the many reasons why the Firebase documentation recommends against using arrays in the database.
But in this case (and most cases that I encounter), you may likely don't really need an array. Say that you just care about what colors your user picked. In that case, you can more efficiently store the colors as a set:
palettes -KSmJZ....A5I "0x474A39": true "0xbA9A7C": true "0xDEDEDF": true "0x141414": true "0x323E35": true