Not counting the Gyarados at Lake of Rage my first one was a Rattata in Crystal, I was excited since it was my first random shiny. I trained it to a pretty high level, sadly it is lost now due to the short lifespan of the battery of Gen 2 games.
Not counting the Red Gyrados, it was a randomly encountered shiny Ratatta in White 2 I found in Castelia Sewers. I transferred it to Gen 7 a while ago.
first encountered a shiny meowth in the battle tower in fire red :') Can't remember my first caught. I wanna say something in Emerald, maybe a Luvdisc
My first shiny was a Golbat found while mucking around in Snowpoint Temple way back when. I had no idea what a shiny even was then, so I thought my game had glitches since I didn't see the sparkle. I found out quickly after catching it and going to a computer what it was though.
My first not story-tied shiny I got was a Togekiss, per Wondertrade, I think. Also had a pretty high level and decent attacks, so I was very lucky.
Zigzagoon, in Sapphire! Then after that, I got a shiny Wurmple in Emerald! ...Then another Wurmple, in Emerald! Then I got a shiny Taillow. In Alpha Sapphire. So I guess what I'm saying is Hoenn really likes me. And despite attempting hunts in other games, ONLY Hoenn likes me
Spinda, in Sapphire. It was my very first shiny encounter in the very first game of my own! He was weak and looked like covered in moss, but he was shiny and therefore he was special I may not have said cartridge around anymore, but as long as I remember what I had there it's almost the same. Memories, I say!
If we don't count the red gyarados (my first was in Silver way back when) or ROMs (a shiny spinda), then my answer would have to be ... spritzee, in a Friend Safari in Y, which I stumbled across purely by accident. It's probably worth it to note this wasn't my first shiny encounter. Actually, my first shiny encounter was a lugia in Crystal that I promptly killed via poison. This was followed by a shiny vulpix in Gold that Roar'd me away and a shiny graveler in Pearl that Exploded on me. :') My luck has since changed after that spritzee, largely because it got so much easier to hunt or breed for shinies, but oh my God, the lead-up to that...
Not counting Red Gyarados, it was a Sandshrew in Sapphire version! I remember being confused, because I thought the Red Gayrados was some special exclusive thing to G/S/C version. I ended up giving it to my SO, as it's their absolute favorite Pokémon~
Buneary in Platinum during Eterna Forest! It took me WHOLE SECONDS TO REALISE I WAS LOOKING AT A SHINY BUNEARY
First shiny 'mon was a numel in Sapphire iirc. I think I killed it since child me didn't know it was anything special. Oops!
A Poliwag in Silver. On a tiny Gameboy Color screen back then, I couldn't tell what the difference actually was, but I knew when I saw the stars I wanted it, so I caught it while on the phone with a friend. He told me that shiny Pokémon look different, so I went to the status screen to examine what might be different about it... I excitedly came to the conclusion that the sprite was backwards! All sprites are flipped on the status screen...
Mine was a shiny Mawile from a raid on Pokémon Go. I caught it the same day I caught my first LV shiny!