Female Shelgon won't breed with Male Gyarados (holding Everstone, Adamant, Dragon Dance) - why?!

Question

The Day care said they do not like each other and I am just trying to figure out what I'm doing wrong.

Answer 1

You're not doing anything wrong, actually.

As stupid as it sounds, those two will breed. As long as the man doesn't say, "The two prefer to play with other Pokémon than each other," then the two you have in the Day Care will breed.

Source: Experience and Bulbapedia

Answer 2

Nothing's wrong.

Actually, the 2 Pokémon will breed even if the man says this. It happened to my Samurott with my Ditto and I had an egg. Though, you have a 20 % of chance at each 256 steps to get an egg, increased to 40 % if you have an Oval Charm. This actually happens because your 2 Pokémon has the same ID number, but are not of the same species.

Actually, Fizz said it all, I just added some extra informations. If you transfer an Adamant Gyarados got from another ID number, simply another game, you can increase the chances of getting your egge.

Source, + Experience, Fizz and my brain.