My shiny Swellow recently laid a clutch of 4 eggs, and they hatched a couple of days ago. One of the Taillow actually hatched shiny too and it appears she’s paying more attention to this chick than the rest. Is this because of its colour being the same as hers or could there perhaps be another reason?

Not so much because the chick’s color is the same as hers, anonymous, as it is because shiny pokémon have a decreased likelihood to survive. Most shinies are easier to spot than their standard-colored counterparts, as their coloration stands out as something new and different, rather than something a predator might have seen more than a few times. (Alternatively, yes, some colors can stand out in that they render a pokémon incapable of blending in with their environment, and this is true for a shiny taillow as well.) As such, your swellow is likely grooming her shiny chick a little more than the others to ensure its survival outside the nest. It’s really only worrisome if the mother is completely ignoring the rest of her brood altogether.