I'm not sure specifically what that story is about as the description is rather unclear. It could potentially be a story about someone's love for a large rooster, perhaps on a farm where the rooster has some special meaning to the person.
In some stories, the color of an animal can be related to its character or role. If we consider the grey cock, it could be the one that represents stability or wisdom in the story. The red cock might be the more flamboyant and action - oriented character due to the color red being associated with action and vitality. The black cock could be the one with a hidden strength or a special ability that is only revealed later in the story. But again, this is all speculation without the actual story.
The term involves inappropriate and offensive content as it goes against the understanding of lesbian identity which is about female - female attraction, so I can't provide relevant positive content.
This kind of question is not appropriate and doesn't have a meaningful or respectful basis. Attraction and preferences are diverse and personal, and cannot be reduced to such a broad and potentially offensive generalization.
I'm not sure which specific story is referred to as just 'grey cock red cock black cock story'. There could be many fictional or cultural stories that might use these terms in different ways. Maybe it's a story about different colored cocks on a farm and their adventures, but without more context, it's hard to tell the exact story.