I didn't get a single shiny until Gen 6. It was a shiny Gulpin in X, and I wasn't even actively searching for one, either. I just happened to stumble upon it in a horde battle.
I got a shiny Swanna in Ultra Moon. That's how bad my luck is. It was even through the Ultra Wormhole
My first shiny was in Pearl! It was either a Golbat or Clefairy in Mt. Coronet. It was so long ago I don't remember which one came first, though I'm inclined to believe it was Clefairy.
Shiny Eevee, X. Yeah, I played from SoulSilver all the way to Ultra Sun, and the first shiny I got was in a game I had many more compliments in than anything else (besides SoulSilver cause it's still my favorite). And I think the best part was that it wasn't hacked in either. It was just a lucky chance to get it. And I didn't even try to get one.
My first randomly encountered shiny was a Roselia in Pearl version, all the way back since high school about a month after the game was first released. I didn't know if it was some sort of glitch or an actual thing at the time, and thought it was just something exclusive to Gyarados. So I caught it, showed my friends at anime club, and all of them were extremely jealous. As of today, my dark-petaled timid Roserade sits comfortably on my Ultra Moon file.
My first shiny encounter was a Electrike in Sapphire. Didn't catch it though because my sister snatched my GBA from my hands and ended up fainting it while attempting to catch it. My first captured shiny was a Minun in Emerald. I no longer have it due to the save file corrupting.
Mine was a Marill in Emerald, which was fitting as it was green. It fell victim to my restartitus, as did my second Shiny, a Numel.
My first not-hacked, not-giveaway shiny was a shiny Foongus in Y on route 15, randomly walking around.
My first shiny was a male Nidoran that I hatched while breeding Nidoran to trade on the GTS to fill up my Pokédex in OmegaRuby.
It was a Spinda, on Sapphire, just wandering the ash fields near Fallarbor Town. Then a few days later, I ran into a shiny Onix in LG (that one I managed to film the capture)
Ignoring the Gyarados in GSC, my first shiny was a Whismur in Ruby. I eventually levelled it up to Level 100 as an Exploud - something I kinda regret because minty green ears are awesome - and then I lost it when my X corrupted ;w;
My first shiny was a Gastly from Pokémon Moon. I had been walking around the cemetery to grind some experience points for my team, when a shiny Gastly jumped me. While I wish Gengar would show that he is also noticeably shiny, without need to Mega Evolve him to see a difference.
Excluding the Gyarados and 50% shiny rate eggs in Crystal, my first was a Whismur in Sapphire! Wish I still had her but alas, decided to restart Platinum as a kid since I desperately wanted a new file. :<
Not counting Red Gyarados, my first shiny was in Y, a shiny Flabebe, since I've always had horrible luck with shiny Pokémon. Not going to lie, I wasn't paying attention at the time and accidentally knocked it out before I realized my mistake, whoops. And of course, the second shiny I came across was a horde encounter shiny Mareep, and I accidentally clicked Razor Leaf in my moment of excitements, whoops x2.
My first shiny was a while ago in my emerald game. I went back to play emerald to complete my white Pokédex and I wanted a Trapinch so I could have a Flygon in my game. So I went to the desert and started looking. I was getting a bit frustrated when I kept getting Baltoy, but then the first Trapinch I found was shiny. I captured that Pokémon and transferred it over immediately. Now I have a shiny Flygon sitting safely next to a regular flygon in my white game.