Which is the fastest Pokemon with regards to lore?

There's only one consistent way to judge this, thanks to how infrequent good Pokedex data is.

In-game Stats

Arcanine has a base speed stat of 95 (Gen 6). Dragonite has a base speed stat of 80. And travels around the world in 16 hours. Compared to most Pokemon, this is rather slow. Using this method, we can see that the fastest pokemon stat-wise are:

  1. Deoxys (Speed) - 180
  2. Ninjask - 160
  3. Mega Alakazam - 150
  4. Mega Aerodactyl - 150
  5. Deoxys (Normal) - 150

So it seems Deoxys (Speed) is much faster than Arcanine. Considering most pokemon do not have detailed notes on their speed, and poke-lore is ridiculously inconsistent it seems going off in-game stats is the best way to go.

We could use the speed values to make an estimte of their actual speeds though, using the data provided about Arcanine and Dragoite

250 / 95 = 2.63mph per base speed

40,075 (Distance around the world) / 16 hours = 1556.25mph. / 80 = 19.45mph per base speed

Our first calculation would give Speed Deoxys (2.63 * 180) = 473.4mph, while our second would give them (19.45 * 180) 3501mph. That would cover the distance of New York to LA in one hour.

In Lore

The Pokemon lore is inconsistent, contradictory, and quite useless, but I shall append some answer to this.

  • Genesect using Extreme-Speed - Quite fast - but no numbers
  • Latios - "Faster than a jet" ((1,555 mph, 2,503 km/h))
  • Pidgeot - Mach 2 speed 2,447 km/h
  • Golduck - Explicitly stated to be the fastest swimmer
  • Ninjask - Moves so fast they are almost Invisible.
    Using information from here, they must move at around 20,000km/h minimum, and from a distance of 10 miles (which is the distance to view the object for it to seem invisible). This is almost impossible from a close distance (If it abides by normal laws of physics, it'd be almost impossible to move so fast as to be almost invisible at a close distance. But if the Dex is to be believed, this is without a doubt the fastest pokemon.)

The question is unanswerable.

Pokémon lore, especially move and Pokédex description, has always been very exaggerated since it's supposed to appeal to children. There has never been any proof that the grandest claims found in the Pokédex are true. For example:

Magcargo's body temperature is approximately 18,000 degrees Fahrenheit.

You'd burst into flames if you so much as looked at one.

Alakazam's brain continually grows, infinitely multiplying brain cells.

Alakazam's head has yet to explode.

[Machamp's] four ruggedly developed arms can launch a flurry of 1,000 punches in just two seconds.

125 punches per arm per second.

Manectric is constantly discharging electricity from its mane. The sparks sometimes ignite forest fires. When it enters a battle, this Pokémon creates thunderclouds.

Manectric does not, in fact, create thunderclouds or discharge constantly.

[Cubone] always wears the skull of its dead mother, so no one has any idea what its hidden face looks like.

I've bred Cubone before, and my Marowak still has a skull, and is definitely alive.

When [Victini] shares the infinite energy it creates, that being's entire body will be overflowing with power.

We've got a being that can produce infinite energy. Not a huge amount, not enough to obliterate the universe, it's literally infinite. I don't need to tell you how ridiculous that is. If any Pokémon is the fastest, it's Victini.

And finally, Quick Attack's description:

The user lunges at the target at a speed that makes it almost invisible.

I guess anything that learns Quick Attack is the fastest Pokémon in existence, if you want to trust the lore, but I prefer this move.