I have been playing Pokemon fire red a lot recently to shiny hunt Pokemon but I can't find a method to do so.
Unfortunately, ways to increase Shiny Odds were introduced in Gen. 4. These included Masuda Method, etc. It is still a 1/8192 chance of encountering a Shiny Pokémon.
However, you can always Soft Reset for a Shiny, or just breed until you get a shiny if you wish.
Hope this helps!