Arcanine are said to travel 6200 miles in a day and night, which comes out to about 250mph. Dragonite are said to break the sound barrier (~750mph), and to be able to fly around the world in .. was it 15 hours? (~1500mph) They're also stated to be the fastest flying Pokemon.
Is there any more information on what speeds Pokemon reach? Either as travel speeds (would be interested in both flying, land, water, and underground), or muscle movement speed (e.g. if it could react to block an attack in a millisecond, and we know roughly how large the Pokemon is so we could guess a distance needed to block, that could give us a speed).
I couldn't find any information on Speed Deoxys, which would be a natural candidate for many records.
Best Answer
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:
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.
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.)