To the furthest extent of my knowledge, whether or not a breeding Pokemon is shiny has no effect on the offspring. The shininess is generated entirely by the RNG. Therefore, breeding 2 shiny Pokemon together doesn't increase the offspring shiny chance.
I don't know the exact shiny rate in Reborn, but it's often quoted as a figure of roughly 1 in 100. Therefore, the chances of breeding shinies in succession are low, but not astronomically so. The shiny charm in Reborn, as in the main series games, doubles the shiny rate; going off the previous figure, that would make it about 1 in 50.