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Trade the Red Gyarados to R/B/Y version and teach Mimic to it (have all of its other moves erased, I believe). Now go encounter a ditto and use mimic to transform into that ditto. Then the ditto will transform, etc. Do it for about 2 or 3 times, I can't really remember. But capture the Ditto afterwards and trade it back to G/S/C. It's supposed to be shiny and you'll have 1/46 chances of having a shiny Pokemon from an egg if you bred with that ditto.
If you're really desperate to get a shiny Ditto, you can still find one wild. They are extremely rare though, so I wouldn't waste time trying to find one.