If you sacrifice a Shiny fighter to another copy of the same variant, the "Shiny" attribute will transfer over. The fighter that received the sacrifice will have its level recalculated according to the halved XP-per-level requirements that all Shiny fighters have. Future skill tree and Marquee Ability upgrades will have their costs halved, but you will not be refunded for already-purchased upgrades. This works whether you are sacrificing the fighter as tier-upgrade material or just for XP and Prestige Ability ranks -- the Sacrifice button will change to include the text "TRANSFER SHINY" to let you know it'll work as desired.
If you sacrifice as Shiny fighter to any other variant (or a matching fighter that is already Shiny), the Shiny status vanishes into nothingness. You lose, you get nothing. Good day, sir.