Traits

Shiny Domesticated (Variant) Pokemon are now one solid base colour, their eyes any shade of blue>cyan, and their markings either one or two colours (sometimes even in a gradient, but only the markings). Something about the Variant gene and Shiny gene presenting at once causes the colour choice to go haywire, and as such there is little to no restriction on what colour the Shiny is. 

Shiny Variants also have a translucent quality to fur or scale/skin, and appear with a shimmery effect, rather than the glittery effect shinies are known for.

Typical Markings + Shiny Variant

Partial Markings + Shiny Variant

Standard Markings + Piebald Mutation + Shiny Variant

Standard Markings + Chimerism Mutation + Shiny Variant. Note that the shimmery effect isn't present on the non Shiny areas. Because the base grading is visible, the Pokemon can still be graded for colour as a normal Variant would. This example is Grade A (colour) + Chimerism + Shiny.

Standard Markings + Shiny

Standard Markings + Piebald Mutation + Shiny. Note that the glittery effect is absent on the white.

Standard Markings + Chimera + Shiny. Note that the glittery effect only affects the Shiny portions of the Chimerism.