As far as I know, there are no direct glitches to do with Shiny Pokemon in GSC. The only thing is that you're able to breed Shiny Pokemon easier with the use of the Shiny Gyarados.
Originally Posted by http://www.pichus-world.com/shiny.php
This is a glitch where you need 2 GBs for. You'll also need a red/blue/yellow cartridge and a link cable.
First, make sure you have any shiny Pokemon on your G/S/C game that appears in R/B/Y and which can learn mimic in R/B/Y (Gyarados is good). Transfer him to a R/B/Y game (the trick will go faster if you delete all his moves but one weak move like leer). On your R/B/Y game, you won't notice any more apart from that your Pokemon is shiny but don't worry, if you transfer him back, he will be shiny again.
Teach him TM 31 (mimic) and go find yourself a wild ditto. Use mimic to learn transform. Ditto will use transform. Let your shiny Pokemon transform into ditto. Wait 'till ditto transforms again. Catch ditto. Transfer him to G/S/C. You now have a blue shiny ditto. Congrats. (The most important thing is that ditto needs to transform twice)
In GSC, the odds of breeding a Shiny egg when using a Shiny parent are 1/64, so by using the Ditto as a parent, this will greatly increase your chances of hatching almost any Shiny Pokemon you like. There's more information on that site I quoted from.