Is it possible to show some pictures or short video/gif to show the differences between your two Inkay cards?
In general, I’ve seen Glossy non-Holo cards a few times: Glossy non-Holo Uncommons cards from the Shining Legends set; these Glossy non-Holo Commons from the Unbroken Bounds set (I own some myself); and I recently saw some Glossy cards from the Pikachu Libre deck (which the seller unfortunately spilled his soda on before he could send them out to me… 
).
So I assume it’s possible with these Shiny Secret Rares as well, although I’ve not seen them yet.
Greetz,
Quuador