How long after mating should i expect eggs from my pokemon? Specifically an arcanine, but does it differ between all pokemon

It really depends on the pokémon, anonymous, but generally speaking, unlike their mammalian counterparts, pokémon can lay eggs as quickly as once a day (much like birds). However, this occurs mainly in pokémon raised specifically for breeding (and, well, all bird pokémon); wild ones and ones trained for other purposes may see eggs once a month to one or two times a year—hence why some of the larger pokémon have mating seasons. Arcanine in particular lay eggs only twice a year, following patterns very similar to estrous cycles in dogs.

Likewise, sometimes, it depends on the individual themselves. Mammalian pokémon generally prefer laying their eggs in places where they feel the safest, and some pokémon find it difficult to like their breeding partners enough to lay eggs together. However, a comfortable female paired with a male she happens to like can achieve that one-egg-a-day pace rather easily.