Pokemon Bank allows Shiny Pokemon in (assuming they are legit). What makes you think it doesn't - a past experience? If so, either that Pokemon was hacked and the hack checker caught it, or it simply screwed up, which unfortunately there is no way to fix (apart from maybe waiting for Nintendo to release an update for the app that fixes any bugs like this).
If anything that was modified makes the Pokemon illegal, then Pokemon Bank will pick it up and stop the Pokemon from getting in. So anything like fake moves, abilities, etc. are found easily and will be stopped right there. The hack checker might also have some way of finding PokeGen Pokemon somewhere in the coding, although I am not sure about this. It don't believe such a thing is possible, and that the only way that Pokemon Bank can find hacked Pokemon is by finding illegal moves, abilities, stats, etc..