You can find color palettes in coloring mode in the white circle with colored dots inside it in the lower left corner of the screen. When you tap on it, the menu with all of the colors and palettes available will open - Gradients, Solid Colors, Live Colors, Recolor palettes, Crayons and My palettes.

Some color palettes are available only for subscribers, but there are some free colors in all palettes (Gradients, Crayons, Solids, Recolor Palettes) so you can test them out.