Well, in X and Y it's a 1/4,096 of getting a shiny... so that's hard already!! :D
And, there are 25 possible natures, so that's a 1/25 shot.
So the answer is simply 1/4,096 x 1/25. So, it's a 1/102,400 chance of getting a Shiny Adamant Charmander. Good luck! :D
Of course, the Everstone breeding technique can take place, to make things a little easier. If one of the parents has an Adamant nature, they can hold an Everstone and the offspring is guaranteed to have it's nature. So it can still be a 1/4096 chance, with the Adamant nature guaranteed. Also, if you use the Masuda Method the chances are increased even more. So, normally it would be a one in a hundred thousand chance but with using the Everstone and the Masuda Method, the odds will still be rare, but hey - if shininess and natures were actually in real life, roughly only 7,000 in the world people would be a Shiny Adamant. x)
As for a normal Adamant Charmander, it would only be a much less overwhelming 1/25 chance since there are only 25 natures. But the aforementioned Everstone can guarantee a normal Adamant Charmander, if one of the parents of the Charmander has an Adamant nature, as well as an Everstone. Hooray for guaranteedness! :D
So yeah. Have fun. :3
Hope I helped. :)
Source and Experience