Yes. The red Gyarados counts in every way, shape, and form as a legitimate shiny Pokémon. It is exactly the same as if you had happened upon a shiny Gyarados rather than a static encounter.
Also, in generation 2, all shiny Pokémon have a 1/64 chance of hatching a shiny Pokémon egg.
A warning: hatching eggs in gen 2 is very slow and tedious because there weren’t any egg o powers or the ability Magma Armor (or any abilities for that matter) so just be patient. Also, you could be really, really unlucky. Trust me, Pokemon feels like it’s rigged very often. I spent almost and entire hour breeding froakies until I found a certain nature with a certain ability. And there’s 18 natures lol. (My brother refused to trade me his own froakie even though he has like 10 he can be really annoying sometimes :/)