Bill: This can happen from time to time, I’m afraid, anonymous. Scientists and breeders alike aren’t quite sure what causes a parent to reject a hatchling, but shininess does indeed seem to increase those chances. It’s thought to be tied into a sort of survival instinct: the more oddly colored a pokémon is, the less likely it will be able to benefit from the advantages its standard coloration provides (camouflage from predators, camouflage from prey, warning patterns, mimicry, etc) in the wild. Therefore, a shiny pokémon tends to be less likely to survive. Additionally, in some cases, shininess may be mistaken for illness, particularly in species whose coloration are lighter than standard or specific colors associated with internal problems (such as yellow being associated with jaundice, especially in humanoid pokémon). Given the color of a shiny torchic, this might be the more likely case—your blaziken might not recognize what a shiny torchic looks like and may think that this hatchling isn’t meant to survive.
Alternatively, it could be something wrong with the mother as well. Just as humans occasionally suffer from postpartum, pokémon mothers may feel the same way, which could result in their inability to even want to care for their offspring. If the birth of this torchic was recent, these feelings may fade away over time, but you’ll need plenty of patience (as well as a temporary surrogate mother to care for the torchic for now) until your blaziken recovers. Support her as much as possible in the meantime and observe her behavior carefully. If/when she feels at ease and safe, reintroduce the chick to see if this is the cause.
The third and final possibility (that I can recall off the top of my head, at least) is that the torchic was separated from its mother far too early. If, for example, you removed the chick from your blaziken for even as little as a few hours after birth or even if you’ve removed the chick from the nest and failed to put it back at night while your blaziken was resting, you may have accidentally interfered with the bonding process. While the entire idea that handling a hatchling with your hands will cause parents to reject their children is a myth for most species, for blaziken, there is a grain of truth to it, especially when they’re extremely young. While your blaziken likely won’t be able to catch your scent on her chick, she will be unlikely to recognize its look or heat signature if it’s not next to her for the first several hours after birth.
Of course, these are only a few possible scenarios out of many. As I’ve said, it’s difficult to tell what the case actually is, and as expressive as pokémon are, they may not be able to convey effectively what’s wrong. You could certainly try (and this would be an excellent idea, actually), but I’m afraid many of the possibilities have rather bleak outcomes. That is to say, if your blaziken has outright rejected this torchic, then it’s likely to have been permanently rejected, and any attempts for reintroduction may actually result in violence from your blaziken. (Many wild blaziken will kill torchic they reject, and this holds true for tame ones as well, as you likely know.) I would advise giving your blaziken a little more time to recover from the excitement of having a torchic hatch, then trying to reintroduce her torchic to her one more time. If she still rejects it, I’m afraid you’ll need to raise the torchic yourself.
Luckily, though, many bird pokémon such as torchic are rather independent, compared to most mammalian pokémon. That is to say, your torchic still has a very strong chance of survival, even without its mother, so long as you’re careful about hand-feeding it and keeping watch on it for the first few months.
Best of luck!
The Pokédex According to Bill 