How do you reroll a sparkling Aniimo's color?

It only works on an Aniimo that is already Sparkling, so it cannot turn a normal one shiny. Each use rolls the colour style again at random. You cannot pick the result, and a specific Sparkling colour is never guaranteed, so a reroll can land on something you like less than what you had.

You buy Sparkling Pigment with Sparkle Seals. Since Sparkling status is purely cosmetic and carries no stat increase, a reroll changes how your Aniimo looks and nothing else about it.

It also works on sparkling Prismana Aniimo. You can make one by applying a Prismana Orb to an Aniimo that is already sparkling, which keeps traits such as Alpha status and perfect potential, and then use Pigment on the result.

What a reroll can land on

Each species has a set of standard Sparkling styles, numbered Type 1 upward. The total is not settled: it is given as 10 and as 12. You can see the full set for any species in the in-game creature index before you spend anything.

Above those sit Dazzling and Shadow, the two rarest Sparkling types, with lower roll chances than Types 1 to 10. Pigment can roll Dazzling. For comparison, catching a wild Aniimo with a Sparkling Cube gives a common style 99% of the time, Dazzling 1% of the time, and never Shadow, so rerolling with Pigment is the other way to chase Dazzling on an Aniimo you already own.

Getting a Sparkling Aniimo to reroll in the first place

Pigment needs a Sparkling Aniimo to work on. You can get one by catching it with a Sparkling Cube, hatching an egg that carries the sparkling mutation (always a sparkling hatch, but prismatic eggs only roll it 0.5% of the time), or spending ten Sparkling Stamps to convert an Aniimo you already have. Sparkling Cubes are scarce, so use them on Aniimo you plan to keep on your team. That also makes them the Aniimo you are most likely to want to recolour later.

Not settled: The number of standard Sparkling styles per species, and so the size of the pool a reroll draws from, is not settled: it is given as 10 and as 12. The facts also don't say whether Pigment can roll the Shadow style.