i actually did a bit of reading about this over the weekend. i'm trying to get shiny eggs too
from what i understood the 1/64 is a giant meme in all in one case: if the egg has a 7/8 male ratio. if you wanted, say, charmander or totodile, you can't just breed the red gyarados with a female of those species. because of the way DV inheritance works, you will *never* get a shiny with that combination. this is because 7/8 male ratio mons can only be shiny if they are male. DVs are inherited from the parent of the opposite gender. therefore, females will always inherit the shiny defense and special DVs needed to be shiny, but because of the minimum requirement for the attack DV, they will cannot be shiny themselves
buuuut this doesn't mean you're fucked - you breed the red gyarados until you get that 1/8 chance female. from there, you can breed that female with something else (not red gyarados, they won't be compatible). eggs from that pairing have a 1/64 chance of being shiny. the mother will have inherited gyarados's defense and special DVs, and attack and speed are generated at random. HP is calculated from the other stats and can be ignored
tl;dr defense and special DVs are key. any female that directly descends from your red gyarados can produce shiny offspring. males that directly descend from your red gyarados will never be shiny
not too sure about gender ratios other than 7/8 male. i'm only trying to get starters right now
