Pokémon with Flame Body are essentially walking incubators. While actual portable incubators exist, pokémon are at least sentient and capable of maintaining and protecting eggs far better and more consistently than an incubator. Or to put it in other words, pokémon possess instincts that allow them to care for eggs by default, and with the amount of crossbreeding each species is capable of, specimens with Flame Body understand that every egg has a different set of needs, whereas humans only have a general idea of such (and incubators don’t typically have any idea of that at all). So when you allow a pokémon with Flame Body to care for an egg, they’re capable of cutting down on incubation time, simply because they not only know how to care for the egg instinctually (and thus know, for example, the type of bedding an egg requires, how to clean it, and so forth), but they also regulate their own body temperature to meet the egg’s needs.

It should be noted that while all pokémon know how to care for an egg, the reason why those with Flame Body are especially good at it is because not every pokémon is capable of emitting and controlling their levels of body heat with the same level of precision as a Flame Body pokémon. Even other fire-types are not quite as exact.

The same goes for pokémon with Magma Armor, surprisingly enough. Perhaps because of their understanding of the makeup of their body, pokémon with Magma Armor are also capable of caring for an egg by way of maintaining the constant, precise temperature needed to hatch it. However, unlike pokémon with Flame Body, Magma Armor specimens do not do so by regulating their own body temperature. Instead, they do so by realizing they perhaps should maintain a very specific distance from said egg.